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Publications of Yury Neretin

1. Books

1. Categories of symmetries and infinite-dimensional groups.
London Mathematical Society Monographs. New Series, 16. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1996. xiv+417, ISBN-13: 978-0198511861; ISBN-10: 0198511868;

2. Lectures of Gaussian integral operators and classical groups. European Mathematical Society, EMS Series of Lectures in Mathematics (2011). ISBN print 978-3-03719-080-7, ISBN online 978-3-03719-580-2, DOI 10.4171/080

3. Moscow seminar in Mathematical Physics, collection of papers, Translations of American Mathematical Society, Series 2, 221, eds. Neretin, Yu.A., Olshanetsky, M.A., Rosly, A. 2007, Print ISBN: 978-0-8218-4371-0, Electronic ISBN: 978-1-4704-3431-1

4. The time of Luzin. The born of Moscow mathematical school. The Soviet mathematics in the context of social upheavals of 1920-30s. (Russian) Editorial URSS, Per aspera ad astra, 53 (2021), ISBN 978-5-9710-7715-2.

5. Beloshapka V.K., Bogachev V.I., Borodin P.A., Domrin A.B., Kashin B.S., Neretin Yu.A., Paramonov P.V., Protasov V.Yu., Ryzhikov V.V.. Sorokin V.N., Fedorovskii K.Yu, Khelemskii A.Ya., Sheipak I.A., Shkalikov A.A.
Function theory and functional analysis. Lectures for postgraduate students, Moscow State University, 2023. ISBN: 978-5-19-011784-4.

2. Theses

Unitary highest weight representations of Virasoro algebra Ph.D. Moscow State University, 1983

Categories enveloping infinite-dimensional groups and representations of category of Riemannian surfaces. Thesis, Russian doctoral degree (Habilitation), Steklov insitute, 1992

3. List of published research papers


  1. Differential operators on Lie groups. (Russian) Uspekhi Mat. Nauk 36 (1981), no. 2(218), 195--196 ; translation in Russ.Math.Surveys, 1981, 36:2, 187--188
    DOI , scan , Russian.
  2. Complementary series of representations of a group of diffeomorphisms of the circle. (Russian) Uspekhi Mat. Nauk 37 (1982), no. 2(224), 213--214. ; translation in Russ.Math.Surveys, v. 37 (1982),289-230
    DOI , Russian.
  3. Unitary representations with a highest weight of a group of diffeomorphisms of a circle. (Russian) Funktsional. Anal. i Prilozhen. 17 (1983), no. 3, 85--86 ; translation in Funct.Anal.Appl., 1983, 17:3, 235--237
    DOI , scan , Russian.
  4. Boson representation of the circle diffeomorphism group. (Russian) Dokl. Akad. Nauk SSSR 272 (1983), no. 3, 528--531; translation in Sov.Math.Dokl., v.28(1983), 411-414.
    Russian.
  5. Unitary representations of the groups of diffeomorphisms of the $p$-adic projective line. (Russian)Funktsional. Anal. Prilozhen. 18 (1984), no. 4, 92--93; translation in Funct.Anal.Appl.,1984, 18:4, 345--346
    DOI , scan , Russian.
  6. (joint with Kirillov A.A.) The variety $A_n$ of structures of $n$-dimensional Lie algebras. (Russian) in Some problems in modern analysis (in the memorz of V.M.Alekseev) (eds. Magaril-Il'yaev, G. G.; Tikhomirov, V. M.) 42--56, Moskov. Gos. Univ., Mekh.-Mat. Fak., Moscow, 1984. English translation in: Fourteen papers translated from the Russian, AMS Translations, 137 (1987) 21-30
    DOI , scan .
  7. Discrete occurrences of representations of the complementary series in tensor products of unitary representations. (Russian) Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 79--80; translation in Funct.Anal.Appl., v.20(1986),68-70
    DOI , scan , Russian.
  8. On the spinor representation of $O(\infty,C)$. (Russian) Dokl. Akad. Nauk SSSR 289 (1986), no. 2, 282--285 ; translation in Sov.Math.Dokl., v.34(1987), 71-74.
    scan , Russian.
  9. An estimate for the number of parameters defining an $n$-dimensional algebra. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 2, 306--318, 447; Math. USSR-Izv. 30 (1988), no. 2, 283--294
    DOI , scan , Russian.
  10. On a complex semigroup containing the group of diffeomorphisms of the circle. (Russian) Funktsional. Anal. i Prilozhen. 21 (1987), no. 2, 82--83; translation in Funct.Anal.Appl., 21 (1987), 160-161
    DOI , scan , Russian.
  11. Almost invariant structures and constructions of unitary representations of the group of diffeomorphisms of the circle. (Russian) Dokl. Akad. Nauk SSSR 294 (1987), no. 1, 37--41. ; translation in Sov.Math.Dokl., v.35(1987), 71-74
    scan , Russian.
  12. Tensor products of unitary representations of $SL_3(R)$. (Russian) Ukrain. Mat. Zh. 40 (1988), no. 2, 240--241, 272; translation in Ukrainian Math. J.40 (1988), no. 2, 207--208
    DOI , scan 1 , scan 2 (Russian).
  13. Holomorphic continuations of representations of the group of diffeomorphisms of the circle. (Russian) Mat. Sbornik 180 (1989), no. 5, 635--657, 720 ; translation in; Russ.Acad.Sci. Sbornik.math., 1990, 67:1, 75--97
    DOI , scan , Russian.
  14. (joint with Nazarov, Maxime and Olshanskii, Grigorii) Semi-groupes engendres par la representation de Weil du groupe symplectique de dimension infinie. (French) [Semigroups generated by the Weil representation of the infinite-dimensional symplectic group] C. R. Acad. Sci. Paris Math. 309 (1989), no. 7, 443--446.
    scan ,
  15. Spinor representation of an infinite-dimensional orthogonal semigroup and the Virasoro algebra. (Russian) Funktsional. Anal. i Prilozhen. 23 (1989), no. 3, 32--44, 96; translation in Functional Anal. Appl. 23 (1989), no. 3, 196--207 (1990)
    DOI , scan , Russian.
  16. Almost invariant structures and related representations of the diffeomorphism group of a circle. in Representation of Lie groups and related topics, eds. D.P. Zhelobenko, A.M.Vershik, 245--267, Adv. Stud. Contemp. Math., 7, Gordon and Breach, New York, 1990.
    In google-book .
  17. On operators that connect the holomorphic representations of different groups. (Russian) Dokl. Akad. Nauk SSSR 312 (1990), no. 6, 1318--1321; translation in Soviet Math. Dokl. 41 (1990), no. 3, 547--550 (1991)
    Russian.
  18. On a semigroup of operators in the boson Fock space. (Russian) Funktsional. Anal. i Prilozhen. 24 (1990), no. 2, 63--73, 96; translation in Functional Anal. Appl. 24 (1990), no. 2, 135--144
    DOI , scan , Russian.
  19. Infinite-dimensional groups, their mantles, trains, and representations. in Topics in representation theory (ed. A.A.Kirillov) 103--171, Adv. Soviet Math., 2, Amer. Math. Soc., Providence, RI, 1991.
    In e-book .
  20. Extension of representations of classical groups to representations of categories. (Russian) Algebra i Analiz 3 (1991), no. 1, 176--202 ; translation in St-Peterburg Math.J, 1992, v.3, 147-170.
    scan , Russian.
  21. Categories of bistochastic measures and representations of some infinite-dimensional groups. (Russian) Mat. Sbornik 183 (1992), no. 2, 52--76; translation in Russian Acad. Sci. Sbornik Math. 75 (1993), no. 1, 197--219
    DOI , scan , Russian.
  22. Universal completions of complex classical groups. (Russian) Funktsional. Anal. i Prilozhen. 26(1992), no. 4, 30--44, 96; translation in Functional Anal. Appl. 26 (1992), no. 4, 254--265 (1993)
    DOI , scan , Russian.
  23. Combinatorial analogues of the group of diffeomorphisms of the circle. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), no. 5, 1072--1085; translation in Russian Acad. Sci. Izv. Math. 41 (1993), no. 2, 337--349
    DOI , scan , Russian.
  24. Mantles, trains and representations of infinite-dimensional groups. First European Congress of Mathematics, Vol. II (Paris, 1992), 293--310, Progr. Math., 120, Birkhauser, Basel, 1994.
    scan
  25. Some remarks on quasi-invariant actions of loop groups and the group of diffeomorphisms of the circle. Comm. Math. Phys. 164 (1994), no. 3, 599--626.
    DOI , scan
  26. (joint with Olshanskii, G. I.) Boundary values of holomorphic functions, singular unitary representations of the groups ${\rm O}(p,q)$ and their limits as $q\to\infty$. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)223 (1995), Teor. Predstav. Din. Sistemy, Kombin. i Algoritm. Metody. I, 9--91, 337; translation in J.Math.Sci (New York) 1997, 87:6, 3983--4035
    DOI , scan , Russian.
  27. Integral operators with Gaussian kernels and symmetries of canonical commutation relations. 'Contemporary mathematical physics'. F. A. Berezin memorial volume, eds. R. L. Dobrushin, R. A. Minlos, M. A. Shubin and A. M. Vershik 97--135, Amer. Math. Soc. Transl. Ser. 2, 175, Amer. Math. Soc., Providence, RI, 1996.
    scan .
  28. The group of diffeomorphisms of a half-line, and random Cantor sets. (Russian) Mat. Sbornik 187 (1996), no. 6, 73--84; translation in Russian Acad. Sci. Sbornik Math. 1996, 187:6, 857--868
    DOI , scan , Russian.
  29. The Hausdorff metric, construction of a separable quotient space, and boundaries of symmetric spaces. (Russian) Funktsional. Anal. i Prilozhen.(1997), no. 1, 83--86; translation in Funct. Anal. Appl., 1997, 31:1, 65--67
    DOI , scan , Russian.
  30. Hinges and Study-Semple-Satake-Furstenberg-De Concini- Procesi boundary in 'Kirillov's Seminar on representation theory'. ed. G.Olshanski AMS Translations, v.181, 1997, 165--230
    scan
  31. On correspondence between the space $L^2$ over Poisson measure and bosonic Fock space Mat.Sbornik, 1997, 11, 19--50; translation in Russian Acad. Sci. Sbornik Math. 188, 11, 1587--1616
    DOI , scan , Russian.
  32. Fractional diffusions and quasiinvariant actions of infinite dimensional groups. Trudy MIRAN (Russian), v.217, 126--173 : English translation in Transactions of Steklov Mathematical Institute, v.217, 1997
    scan , Russian.
  33. Boundary values of holomorphic functions and discrete spectra in noncommutative harmonic analysis, Proceedings of School 'Analysis on homogeneous spaces', Tambov, 1996; publilshed in 'Vestnik Tambovskogo Universiteta', 1997 (English)
    cyberleninka , .ps .
  34. Restriction of function which is holomorphic in a domain to a curve lying in the boundary and discrete $SL_2(R)$-spectra. Izv. Ross. Akad. Nauk Ser. Mat. 62 (1998), no. 3, 67--86; translation in Izv. Math. 62 (1998), no. 3, 493--513
    DOI , scan , Russian.
  35. Supercomplete bases in the space of symmetric functions. Funkts.Anal i prilozh., (1998), no. 1,12--28, 96; translation in Funct. Anal. Appl. 32 (1998), no. 1, 10--22
    DOI , scan , Russian.
  36. Krein--Schmullian generalized fractional linear maps and conformal geometry of symmetric spaces Mat.Sbornik, 90 (1999), no. 2,93--122 translation in Sb. Math. 190 (1999), no. 1-2, 255--283
    DOI , scan , Russian.
  37. Boundary values of holomorphic functions and some spectral problems for unitary representations. In collection J.Hilgert, J.D.Lawson, K.-H.Neeb, E.B.,Vinberg (eds.) 'Positivity in Lie groups', W. de Gruiter, 1998, pp.221--248
    DOI , arXiv,
  38. A remark on boson-fermion correspondence Reports of Math.Phys, 1999, 43 (1999), no. 1-2, 267--269.
    DOI , arXiv.
  39. Notes on affine isometric actions of discrete groups in ' Analysis on infinite dimensional groups and algebras.' eds. H.Heyer, J.Marion, World scientific, 1999, pp. 274--320.
    arXiv
  40. Pseudoriemannian symmetric spaces: uniform realizations and open embeddings to Grassmanians Zap.Nauchn. Seminar. PO MIRAN, 1999(Russian); English translation in J. Math.Sci (N.Y), 2001, 107:5, 4248--4264)
    DOI , arXiv, Russian.
  41. Matrix analogs of B-functions and Plancherel formula for Berezin kernels Sbornik. Math. 191, 200, 683--715; translation in Sb. Math., 191:5 (2000), 683-715
    DOI , arXiv, Russian.
  42. On the separation of spectra in the analysis of Berezin kernels. (Russian) Funktsional. Anal. i Prilozhen. 34 (2000), no. 3, 49--62, 96; translation in Funct. Anal. Appl. 34 (2000), no. 3, 197--207
    DOI , arXiv, Russian.
  43. On Jordan angles and the triangle inequality in Grassmann manifolds. Geom. Dedicata 86 (2001), no. 1-3, 81--92.
    DOI , arXiv.
  44. Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants. Mosc. Math. J. 1 (2001), no. 2, 157--220, 303.
    DOI , arXiv.
  45. Plancherel formula for Berezin deformation of $L^2$ on Riemannian symmetric space. J. Funct. Anal. 189 (2002), no. 2, 336--408.
    DOI , arXiv,
  46. Index hypergeometric transformation and an imitation of analysis of Berezin kernels on hyperbolic spaces Mat. Sb., 192, No. 3, 83--114 (2001); English translation in Russian Acad. Sci. Sb. Math., 192, 403--432.
    DOI , arXiv, Russian.
  47. Hua-type integrals over unitary groups and over projective limits of unitary groups. Duke Math. J. 114 (2002), no. 2, 239--266
    DOI , arXiv,
  48. Beta integrals and finite orthogonal systems of Wilson polynomials. (Russian) Mat. Sb. 193 (2002), no. 7, 131--148; translation in Sb. Math. 193 (2002), no. 7-8, 1071--1089
    DOI , arXiv, Russian.
  49. Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 292 (2002), Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 7, 62--91, 178--179. Reprinted in J. Math. Sci. (N. Y.) 126 (2005), no. 2, 1077-1094
    DOI , arXiv, site of journal.
  50. The action of an overalgebra in the Plancherel decomposition and shift operators in an imaginary direction. Izv. Ross. Akad. Nauk Ser. Mat. 66(2002), no. 5, 171--182; translation in Izv. Math. 66 (2002), no. 5, 1035--1046
    ( arXiv, Russian , DOI )
  51. A construction of finite-dimensional faithful representation of Lie algebra. Proceedings of the 22nd Winter School "Geometry and Physics" (Srni, 2002). Rend. Circ. Mat. Palermo (2) Suppl. No. 71 (2003), 159--161.
    arXiv , journal
  52. Groups of hierarchomorphisms of trees and related Hilbert spaces.
    J. Funct. Anal. 200 (2003), no. 2, 505--535. DOI , arXiv,
  53. Geometry of $GL_n(C)$ at infinity: hinges, complete collineations, projective compactifications, and universal boundary. in 'The orbit method in geometry and physics (Marseille, 2000)', ed. C. Duval, L. Guieu and V. Ovsienko. 297--327,
    DOI , arXiv,
  54. Rayleigh triangles and nonmatrix interpolation of matrix beta integrals. Mat. Sb. 194 (2003), no. 4, 49--74; translation in Sb. Math. 194 (2003), no. 3-4, 515--540
    DOI , arXiv, Russian
  55. . Pencils of geodesics in symmetric spaces, Karpelevich boundary,and associahedron-like polyhedra. in Lie groups and symmetric spaces. In memory of F. I. Karpelevich. , ed S.Gindikin, 225--255, Amer. Math. Soc. Transl. Ser. 2, 210, Amer. Math. Soc., Providence, RI, 2003.
    DOI , arXiv,
  56. The beta function of the Bruhat-Tits building and the deformation of the space $l\sp 2$ on the set of $p$-adic lattices. Mat. Sb. 194 (2003), no. 12, 31--62; translation in Sb. Math. 194 (2003), no. 11-12,1775--1805
    DOI , arXiv, Russian
  57. Structures of boson and fermion Fock spaces in the space of symmetric functions. Acta Appl. Math. 81 (2004), no. 1-3, 233--268.
    DOI , arXiv
  58. (joint with Foth, T.) Zak transform, Weil representation, and integral operators with theta-kernels. Int. Math. Res. Not. 2004, no. 43, 2305--2327.
    arXiv, DOI
  59. Some continuous analogs of expansions in Jacobi polynomials and vector valued hypergeometric orthogonal bases Funct. Anal. Appl., 2005, 39:2, 106-119
    DOI , arXiv, Russian
  60. On compression of Bruhat-Tits buildings, Zap. Nauchn. Seminar. POMI RAN, 325(2005), 163--170 ; translation in J. Math. Sci. (N. Y.) 138 (2006), no. 3, 5722-5726
    DOI , arXiv, Russian
  61. Stable densities and operators of fractional differentiation, in Representation theory, dynamical systems, and asymptotic combinatorics, eds/ V. Kaimanovich, A. Lodkin, 117-137, Amer. Math. Soc. Transl. Ser. 2, 217, Amer. Math. Soc., Providence, RI, 2006.
    DOI , arXiv
  62. Fractional diffussions, group of diffeomorphisms of circle and loop groups. in Seminar GLOBUS, eds. M.Tsfasman, V.Prasolov, 2005 (Russian), 64--81
    here
  63. Perturbation of Jacobi polynomials and piesewise hypergeometric orthogonal systems Mat.Sbornik 51--78 (Russian); English transl.: Sbornik, Mathematics, 2006, v.197, N 11, 1607--1633
    DOI , arXiv, Russian
  64. Central extensions of groups of symplectomorphisms, Moscow Math.J., V. 6 (2006), Number 4, 703--729,
    DOI , arXiv
  65. Perelomov problem and inversion of Segal--Bargmann transform. Funct. Anal. Appl., 2006, N 4, 330--333
    DOI , arXiv, Russian
  66. Stein--Sahi representations and some problems of harmonic analysis, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 331 (2006), 125--169; translation in Journal of Mathematical Sciences (New York), 2007, 141:4, 1452-1478
    DOI , arXiv, Russian
  67. Airault, H.; Neretin, Yuri A. On the action of Virasoro algebra on the space of univalent functions. Bull. Sci. Math. 132, No. 1, 27-39 (2008)
    DOI , arXiv
  68. On adelic model of boson Fock space. in Neretin, Yu., Olshanetsky, M., Rosly A.(eds.), Moscow Seminar in mathematical physics, II. Providence, RI: American Mathematical Society (AMS). Translations. Series 2. American Mathematical Society 221. Advances in the Mathematical Sciences 60, 193-202 (2007).
    DOI , arXiv.
  69. Determinantal point processes and fermionic Fock space. in Neretin, Yu., Olshanetsky, M., Rosly A.(eds.), Moscow Seminar in mathematical physics, II. Providence, RI: American Mathematical Society (AMS). Translations. Series 2. American Mathematical Society 221. Advances in the Mathematical Sciences 60, 185-191 (2007)
    DOI , arXiv.
  70. Matrix elements of irreducible Harish-Chandra modules are hypergeometric. Funktsional. Anal. i Prilozhen. 41 (2007), no. 4, 60--69, 96; translation in Funct. Anal. Appl. 41 (2007), no. 4, 295-302
    DOI , paper, Russian
  71. Ramified integrals, Casselman phenomenon, and holomorphic continuations of group representations. in Analysis and mathematical physics (eds. B. Gustafsson, A. Vasil'ev), 427-439, Trends Math., Birkhauser, Basel, 2009.
    DOI , arXiv.
  72. Beta-function of tube of the light cone Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 378 (2010), Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 73-80; reprinted in J. Math. Sci. (N. Y.), 174:1 (2011), 36-40
    DOI , arXiv, Russian
  73. On spherical functions on the group ${\rm SU}(2)\times{\rm SU}(2)\times{\rm SU}(2)$. Funktsional. Anal. i Prilozhen. 44 (2010), no. 1, 59--67; translation in Funct. Anal. Appl. 44 (2010), no. 1, 48-54 (arXiv,
    DOI , arXiv, Russian
  74. Double cosets for $\SU(2)\times...\times\SU(2)$ and outer automorphisms of free groups Int. Math. Res. Notices, 2011, 9, 2047--2067.
    arXiv, DOI)
  75. Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories. Int Math Res Notices (2012) 2012, no. 3, 501--523.
    (arXiv, DOI)
  76. Spectral data for pairs of matrices of order 3 and action of the group $GL(2,Z)$ Izv. RAN. Ser. Mat., 75:5 (2011), 93-102; Izv. Math., 75:5 (2011), 959-969
    DOI , arXiv, Russian
  77. Sphericity and multiplication of double cosets for infinite-dimensional classical groups. Funct. Anal. Appl., 45:3 (2011), 225-239; translation in Funct. Anal. Appl., 2011, 45:3, 225-239
    DOI , arXiv, Russian
  78. Stein--Sahi complementary series and their degenerations In Representation theory, complex analysis, and integral geometry (eds. B. Krotz, O.Offen and E. Sayag), 133-183, Birkhauser/Springer, New York, 2012.
    DOI , arXiv.
  79. Multi-operator colligations and multivariate characteristic functions Analysis and Mathematical Physics, 1 (2011), no. 2-3, 121-138.
    (arXiv, DOI)
  80. Symmetries of Gaussian measures and operator colligations J. Funct. Anal. 263 (2012), no. 3, 782-802
    (arXiv, DOI)
  81. A remark on representations of infinite symmetric groups Zap. Nauchn.Semin.POMI
    DOI , arXiv, Russian
  82. On topologies on Malcev completions of braid groups Moscow Mathematical Journal, 2012, v.12, N4, pp. 803-824
    DOI , arXiv.
  83. Index hypergeometric integral transform Preprint, Russian version is published as an addendum to Russian edition of G.E.Andrews, R.Askey, and R.Roy "Special functions", MCCME, Moscow, 2013, 607-624
    arXiv, Russian
  84. On the boundary of the group of transformations leaving a measure quasi-invariant", Mat. Sb., 204:8 (2013), 83-116; Sb. Math., 204:8 (2013), 1161-1194
    DOI , arXiv, Russian
  85. Difference Sturm--Liouville problems in the imaginary direction J. Spectral theory, V 3 (2013), № 3, p. 237-269
    DOI (arXiv
  86. Hua measures on the space of $p$-adic matrices and inverse limits of Grassmannians , Izv. RAN. Ser. Mat., 77:5 (2013), 95-108; Izv. Math., 77:5 (2013), 941-953
    DOI , arXiv, Russian
  87. (with D. V. Alekseevsky, P. W. Michor) Rolling of Coxeter polyhedra along mirrors in Geometric methods in physics. Papers from the XXXI Workshop (WGMP) held in Bialowieza, June 24-30, 2012. Edited by P. Kielanowski, S. T. Ali, A. Odesskii, A. Odzijewicz, M. Schlichenmaier, Th. Voronov. Trends in Mathematics. Birkhauser/Springer, Basel, 2013, pp 67-86.
    DOI , arXiv
  88. The space $L^2$ on semi-infinite Grassmannian over finite field Adv. Math. 250 (2014), 320-350.
    DOI arXiv
  89. (with G. Marmo, P. W. Michor) The Lagrangian Radon Transform and the Weil representation J.Fourier Anal. Appl., 2014
    DOI (arXiv )
  90. On an infinite-dimensional limit of the Steinberg representations. Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 126-132; J. Math. Sci. (N. Y.), 200:6 (2014), 718-721
    DOI , arXiv, English
  91. Biinvariant functions on the group of transformations leaving a measure quasiinvariant, Mat. Sb., 205:9 (2014), 145-160; Sb. Math., 205:9 (2014), 1357-1372
    DOI , arXiv, Russian.
  92. Hua type beta-integrals and projective systems of measures on flag spaces IMRN, 2015, no. 21 (2015), 11289-11301, doi: 10.1093/imrn/rnv031
    DOI , arXiv
  93. Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings, Izv. RAN. Ser. Mat., 79:3 (2015), 87-130; Izv. Math., 79:3 (2015), 512-553.
    DOI , arXiv, Russian
  94. Infinite symmetric groups and combinatorial constructions of topological field theory type, Uspekhi Mat. Nauk, 70:4(424) (2015), 143-204; Russian Math. Surveys, 70:4 (2015), 715-773
    DOI , arXiv, Russian
  95. Matrix beta-integrals: an overview in Geometric methods in physics. Proceedings of the XXXIII Workshop (WGMP) held in Bialowieza, June 29-July 5, 2014 (eds. P. Kielanowski, P. Bieliavsky, A. Odzijiewicz, M. Schlichenmaier, Th. Voronov). Trends in Mathematics. Birkhauser/Springer, Cham, 2015, pp. 257-272
    DOI , arXiv https://arxiv.org/abs/1411.2110
  96. On sphericity of the subgroup $PSL(2,R)$ in the group of diffeomorphisms of the circle. Funktsional. Anal. i Prilozhen., 50:2 (2016), 91-94; Funct. Anal. Appl., 50:2 (2016), 160-162
    DOI , arXiv, Russian
  97. Several remarks on groups of automorphisms of free groups, Zapiski Nauchn. Semin. POMI, 2015, v.436, 189-198; Journal of Mathematical Sciences (New York), 2016, 215:6, 748-754
    DOI , arXiv, Russian
  98. On $p$-adic colligations and 'rational maps' of Bruhat-Tits trees in Geometric methods in physics. Papers based on the XXXIV Workshop (WGMP) held in Bialowieza, June 28-July 4, 2015. (eds. P. Kielanowski, S. T. Ali, P. Bieliavsky, A. Odzijewicz, M. Schlichenmaier, Th. Voronov), Trends in Mathematics. Birkhauser/Springer, [Cham], 2016, p.139-158
    DOI , arXiv.
  99. Wishart--Pickrell distributions and closures of group actions Zapiski nauchn. semin. POMI RAN, v. 448, p. 236-245 (Russian); English version in J.Math,Sci. (N-Y), 224:2 (2017), 328-334
    DOI , arXiv, Russian
  100. Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions Izvestiya: Mathematics, 2016, 80:6, 1118-1130
    DOI , arXiv, Russian
  101. Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument Funktsional. Anal. i Prilozhen., 51:2 (2017), 25-41; translation in Funct. Anal. Appl., 51, 2, 2017, 98-111
    DOI , arXiv, Russian
  102. The group of diffeomorphisms of the circle: reproducing kernels and analogs of spherical functions Journal of geometric mechanics, v.9, 2 (2017), 207-225
    DOI , arXiv
  103. Projectors separating spectra for $L^2$ on pseudounitary groups $U(p,q)$ International Mathematics Research Notices, Volume 2019, Issue 17, September 2019, Pages 5256-5283
    DOI , arXiv.
  104. (with A. A. Gaifullin) 102. Infinite symmetric group and bordisms of pseudomanifolds Journal of Topology and Analysis, 2017,
    DOI , arXiv, paper
  105. The Fourier transform on the group $GL_2(R)$ and the action of the overalgebra $\mathfrak{gl}_4$ Journal of Fourier Analysis and Applications, v. 25, p.488-505 (2019)
    DOI , arXiv
  106. (with L. Funar) Diffeomorphisms groups of Cantor sets and Thompson-type groups Compos. math., 154 (2018), no. 5, 1066-1110.
    DOI , arXiv
  107. Combinatorial encoding of infinite symmetric groups and description of semigroups of double cosets Zap. Nauchn. Sem. POMI, 462, POMI, St. Petersburg, 2017, 65-92; J. Math. Sci. (N. Y.), 232:2 (2018), 138-156
    DOI , English
  108. Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra Algebras and representation theory 21 (2018), no. 5, 1087-1117.
    DOI , arXiv
  109. Operational calculus for Fourier transform on the group $GL(2,R)$ Funktsional. Anal. i Prilozhen., 52:3 (2018), 42-52; translation in Funct. Anal. Appl., 2017
    DOI , arXiv, Russian
  110. On the group of infinite $p$-adic matrices with integer elements Zapiski nauchn. semin. POMI RAN, v. 468, 2018, 105-125 (Journal of Mathematical Science, August 2019, Volume 240, Issue 5, pp 572-586).
    DOI , arXiv, English
  111. After Plancherel formula. In Geometric Methods in Physics. XXXVI Workshop and Summer School, Bialowieza, Poland, 2017. Editors: Kielanowski, P., Odzijewicz, A., Previato, E., Trends Math,, 389-401, Birkhauser, 2019.
    DOI , arXiv
  112. A remark on nilpotent Lie algebras that do no admit gradings Zap. Nauchn. Sem. POMI, 481 (2019); Journal of Mathematical Sciences, 247, 711-722(2020).
    DOI , paper .
  113. An analog of the Dougall formula and of the de Branges--Wilson integral Ramanujan Journal, 54 (2021), no. 1, 93-106.
    DOI , arXiv,
  114. Barnes-Ismagilov integrals and hypergeometric functions of the complex field SIGMA, 2020, Volume 16, 072, 20 pages
    DOI , arXiv,
  115. Fourier transform on the Lobachevsky plane and operational calculus Funktsional. Anal. i Prilozhen., 54:4 (2020), 64-73; translation in Funct. Anal. Applications, v 54,4 (2020), 278-286
    DOI , arXiv , Russian.
  116. Polyhomomorphisms of locally compact groups Mat. Sb., 212:2 (2021), 53-80; translation in Sb. Math., 212:2 (2021), 185-210
    DOI , arXiv , Russian.
  117. On the group of spheromorphisms of the homogeneous non-locally finite tree. Izv. RAN. Ser. Mat., 84:6 (2020), 131-164; translation in Izv. Math., 84:6 (2020), 1161-1191
    DOI , arXiv , Russian.
  118. (with V.F. Molchanov) A pair of commuting hypergeometric operators on the complex plane and bispectrality J. Spectr. Theory 11 (2021), no. 2, 509-586,
    DOI , arXiv,
  119. On double cosets of groups GL(n) with respect to subgroups of block strictly triangular matrices Linear and Multilinear Algebra, DOI:10.1080/03081087.2021.1892023
    DOI , arXiv,
  120. Groups $GL(\infty)$ over finite fields and multiplications of double cosets J. Algebra 585 (2021), 370-421, DOI , arXiv,
  121. Description of unitary representations of the group of infinite $p$-adic integer matrices, Represent. Theory 25 (2021), 606-643,
    DOI arXiv.
  122. On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees. Groups Geom. Dyn. 15 (2021), no. 3, 801-824.
    DOI, arXiv,
  123. On a $\mathbb C^2$-valued integral index transform and bilateral hypergeometric series Integral transforms and special functions, 33 (2022), no. 10, 827–845.
    DOI:10.1080/10652469.2022.2050721, arXiv
  124. Inner functions of matrix argument and conjugacy classes in unitary groups. Sb. Math., 213:8 (2022), 1041-1057.
    DOI: https://doi.org/10.4213/sm9673, arXiv
  125. Symmetric groups and checker triangulated surfaces
    In Teichmuller Theory and Grothendieck-Teichmuller Theory (eds. Lizhen Ji, Athanase Papadopoulos, Weixu Su), 169-190, Higher Education Press, China, 2022, ISBN 978-7-04-057638-2
    Preprint version: https://arxiv.org/abs/1710.11565
  126. On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups Mathematical Notes, 2023, 114: 4, 583-592.
    arXiv
  127. On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions Ramanujan Journal, Volume 64, 37-55, (2024) DOI:10.1007/s11139-023-00804-3. Preprint version: https://arxiv.org/abs/2212.09112
  128. Gauss--Berezin integral operators, spinors over supergroup $OSp(2p|2q)$, and Lagrangian super-Grassmannian In Symmetry in geometry and analysis, eds. M.Pevzner, H.Sekiguchi, Springer, to appear. Preprint version: https://arxiv.org/abs/0707.0570
  129. On Derkachov--Manashov $R$-matrices for the principal series of unitary representations, J. Math. Phys., 65, 051701 (2024), https://doi.org/10.1063/5.0175714,
    Preprint version, https://arxiv.org/abs/2306.08389
  130. On the group of homeomorphisms of the Basilica, To appear, Topology Proceedings, Preprint
    https://arxiv.org/abs/2303.11482
  131. Non-singular actions of infinite-dimensional groups and polymorphisms
    , To appear Mosc. Math. J., https://arxiv.org/abs/2301.01736
  132. Symmetric groups and checker triangulated surfaces
    To appear, Mosc. Math. J., https://arxiv.org/abs/1710.11565

4. Submitted papers and preprints

5. Preprints that were not published as papers

6. Essays about outstanding mathematicans

7. Mathematical didactics and education polytics

8. Congratulations

9. Prefaces

10. Interview



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