Papers of Yury Neretin

List of published papers

1. Differential operators on Lie groups.

2. Complementary series of representations of a group of diffeomorphisms of the circle.

3. Unitary representations with a highest weight of a group of diffeomorphisms of a circle.

4. Boson representation of the circle diffeomorphism group.

5. Unitary representations of the groups of diffeomorphisms of the $p$-adic projective line.

6. (joint with Kirillov A.A.) The variety $A_n$ of structures of $n$-dimensional Lie algebras.

7. Discrete occurrences of representations of the complementary series in tensor products of unitary representations.

8. On the spinor representation of ${\rm O}(\infty,{\bf C})$.

9. An estimate for the number of parameters defining an $n$-dimensional algebra.

10. On a complex semigroup containing the group of diffeomorphisms of the circle.

11. Almost invariant structures and constructions of unitary representations of the group of diffeomorphisms of the circle.

12. Tensor products of unitary representations of ${\rm SL}\sb 3({\bf R})$.

13. Holomorphic continuations of representations of the group of diffeomorphisms of the circle.

14 (joint with Nazarov, Maxime and Olshanskii, Grigorii) Semi-groupes engendres par la representation de Weil du groupe symplectique de dimension infinie.

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)

16. Almost invariant structures and related representations of the diffeomorphism group of a circle.

17. On operators that connect the holomorphic representations of different groups.

18. On a semigroup of operators in the boson Fock space.

19. Infinite-dimensional groups, their mantles, trains, and representations.

20. Extension of representations of classical groups to representations of categories.

21. Categories of bistochastic measures and representations of some infinite-dimensional groups.

22. Universal completions of complex classical groups.

23. Combinatorial analogues of the group of diffeomorphisms of the circle.

24. Mantles, trains and representations of infinite-dimensional groups.

25. Some remarks on quasi-invariant actions of loop groups and the group of diffeomorphisms of the circle.

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 $q\to\infty$.

27. Integral operators with Gaussian kernels and symmetries of canonical commutation relations.

28. The group of diffeomorphisms of a ray, and random Cantor sets.

29. The Hausdorff metric, construction of a separable quotient space, and boundaries of symmetric spaces.

30. Hinges and Study-Semple-Satake-Furstenberg-De Concini- Procesi boundary

31. On correspondence between the space $L^2$ over Poisson measure and bosonic Fock space

32. Fractional diffusions and quasiinvariant actions of infinite dimensional groups.

33. Boundary values of holomorphic functions and discrete spectra in noncommutative harmonic analysis,

34. Restriction of function which is holomorphic in a domain to a curve lying in the boundary and discrete $SL_2({\Bbb R})$-spectra.

35. Supercomplete bases in the space of symmetric functions.

36. Krein--Schmullian generalized fractional linear maps and conformal geometry of symmetric spaces

37. Boundary values of holomorphic functions and some spectral problems for unitary representations.

38. A remark on boson-fermion correspondence

39. Notes on affine isometric actions of discrete groups.

40. Pseudoriemannian symmetric spaces: uniform realizations and open embeddings to Grassmanians

41 Matrix analogs of B-functions and Plancherel formula for Berezin kernels

41 On the separation of spectra in the analysis of Berezin kernels.

42. On Jordan angles and the triangle inequality in Grassmann manifolds.

43. Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants.

44. Plancherel formula for Berezin deformation of $L\sp 2$ on Riemannian symmetric space.

45. Index hypergeometric transformation and an imitation of analysis of Berezin kernels on hyperbolic spaces

46. Hua-type integrals over unitary groups and over projective limits of unitary groups.

47. Beta integrals and finite orthogonal systems of Wilson polynomials.

48. Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation.

49. The action of an overalgebra in the Plancherel decomposition and shift operators in an imaginary direction.

50 A construction of finite-dimensional faithful representation of Lie algebra.

51. Groups of hierarchomorphisms of trees and related Hilbert spaces.

52. Geometry of ${\rm GL}\sb n({\Bbb C})$ at infinity: hinges, complete collineations, projective compactifications, and universal boundary.

53 Rayleigh triangles and nonmatrix interpolation of matrix beta integrals.

54. Pencils of geodesics in symmetric spaces, Karpelevich boundary,and associahedron-like polyhedra.

55. The beta function of the Bruhat-Tits building and the deformation of the space $l\sp 2$ on the set of $p$-adic lattices.

56. Structures of boson and fermion Fock spaces in the space of symmetric functions.

57. (joint with Foth, T.) Zak transform, Weil representation, and integral operators with theta-kernels.

58. Some continuous analogs of expansions in Jacobi polynomials and vector valued hypergeometric orthogonal bases

59. On compression of Bruhat-Tits buildings,

60. Some remarks on stable densities and operators of fractional differentiation,

61. Fractional diffussions, group of diffeomorphisms of circle and loop groups.

62. Perturbation of Jacobi polynomials and piesewise hypergeometric orthogonal systems

63. Central extensions of groups of symplectomorphisms,

64. Perelomov problem and inversion of Segal--Bargmann transform.

65. Stein--Sahi representations and some problems of harmonic analysis,

67.Airault, H.; Neretin, Yuri A. On the action of Virasoro algebra on the space of univalent functions.

68. On adelic model of boson Fock space.

69. Determinantal point processes and fermionic Fock space.

70. Matrix elements of irreducible Harish-Chandra modules are hypergeometric.

71. Ramified integrals, Casselman phenomenon, and holomorphic continuations of group representations.

72. Beta-function of tube of the light cone

73. On spherical functions on the group ${\rm SU}(2)\times{\rm SU}(2)\times{\rm SU}(2)$.

74. Double cosets for $\SU(2)\times...\times\SU(2)$ and outer automorphisms of free groups

75. Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories.

76. Spectral data for pairs of matrices of order 3 and action of the group $GL(2,Z)$

77. Sphericity and multiplication of double cosets for infinite-dimensional classical groups.}

78. Stein--Sahi complementary series and their degenerations

79. Multi-operator colligations and multivariate characteristic functions

80. Symmetries of Gaussian measures and operator colligations

Submitted papers and preprints

On the boundary of the group of transformations leaving a measure quasi-invariant"

Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings

Infinite symmetric group and combinatorial descriptions of semigroups of double cosets

Difference Sturm--Liouville problems in the imaginary direction

On topologies on Lie braid groups

Gauss--Berezin integral operators, spinors over supergroup $OSp(2p|2q), and Lagrangian super-Grassmannian

Rolling of Coxeter polyhedra along mirrors

A remark on representations of infinite symmetric groups

Preprints that were not published as papers

On Statistical Researches of Parliament Elections in the Russian Federation, 04.12.2011

Some remarks on separated quotients,

Constructions on boundaries of symmetric spaces,

Perturbations of some classical hypergeometric orthogonal systems, 2003

Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations

Essays about outstanding mathematicans

(joint with S. M. Khoroshkin) Mathematical works of D.P. Zhelobenko.

'Method of second quatization of Berezin'. View 40 years after.

Felix Alexandrovich Berezin and his work

Mathematical didactics and education polytics

Problems on mathematical analysis.

Incredible coincidences and Morozov--Fomenko problem on historical folds.

Snow-ball technology in education,

Unified state examination in Russia: influence and evolution.

Entrance examination patience. Russia and West.

Why it is impossible to write variants of Unified State Examination?

Trandiness of Establishment and engineering education. Spring 2011

A logical problem. Which are purposes of Unified State Examination?

Elections in Russia: falsified mathematics againist electorial falsifications

Congratulations

Mark Iosifovich Graev (to 85 anniversary)

Sabir Medgidovich Gusein-Zade