@article {AP14,
    AUTHOR = {Avdeev, R. S. and Petukhov, A. V.},
     TITLE = {Spherical actions on flag varieties},
   JOURNAL = {Mat. Sb.},
  FJOURNAL = {Matematicheski\u{\i} Sbornik},
    VOLUME = {205},
      YEAR = {2014},
    NUMBER = {9},
     PAGES = {3--48},
      ISSN = {0368-8666},
   MRCLASS = {14L30 (14M15 14M27)},
  MRNUMBER = {3288423},
MRREVIEWER = {Dmitry A. Timash\"{e}v},
       DOI = {10.1070/sm2014v205n09abeh004416},
}

@article {AP20,
    AUTHOR = {Avdeev, Roman and Petukhov, Alexey},
     TITLE = {Branching rules related to spherical actions on flag
              varieties},
   JOURNAL = {Algebr. Represent. Theory},
  FJOURNAL = {Algebras and Representation Theory},
    VOLUME = {23},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {541--581},
      ISSN = {1386-923X},
   MRCLASS = {20G05 (14M15 14M27 22E46)},
  MRNUMBER = {4109129},
MRREVIEWER = {Paolo Bravi},
       DOI = {10.1007/s10468-019-09857-9},
}

@inproceedings {BGG75,
    AUTHOR = {Bern\v{s}te\u{\i}n, I. N. and Gel'fand, I. M. and Gel'fand, S. I.},
     TITLE = {Differential operators on the base affine space and a study of
              g-modules},
 BOOKTITLE = {Lie groups and their representations ({P}roc. {S}ummer
              {S}chool, {B}olyai {J}\'{a}nos {M}ath. {S}oc., {B}udapest, 1971)},
     PAGES = {21--64},
 PUBLISHER = {Halsted Press, New York-Toronto, Ont.},
      YEAR = {1975},
   MRCLASS = {22E45},
  MRNUMBER = {578996},
MRREVIEWER = {James E. Humphreys},
}


@book {Bjorner.Brenti,
    AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363},
      ISBN = {978-3540-442387; 3-540-44238-3},
   MRCLASS = {05-01 (05E15 20F55)},
  MRNUMBER = {2133266},
MRREVIEWER = {Jian-yi Shi},
}

@book {B02,
    AUTHOR = {Bourbaki, Nicolas},
     TITLE = {Lie groups and {L}ie algebras. {C}hapters 4--6},
    SERIES = {Elements of Mathematics (Berlin)},
      NOTE = {Translated from the 1968 French original by Andrew Pressley},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2002},
     PAGES = {xii+300},
      ISBN = {3-540-42650-7},
   MRCLASS = {17-01 (00A05 20E42 20F55 22-01)},
  MRNUMBER = {1890629},
       DOI = {10.1007/978-3-540-89394-3},
}

@book {B91,
    AUTHOR = {Borel, Armand},
     TITLE = {Linear algebraic groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {126},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1991},
     PAGES = {xii+288},
      ISBN = {0-387-97370-2},
   MRCLASS = {20-01 (20Gxx)},
  MRNUMBER = {1102012},
MRREVIEWER = {F. D. Veldkamp},
       DOI = {10.1007/978-1-4612-0941-6},
}

@incollection {Brion.Lectures,
    AUTHOR = {Brion, Michel},
     TITLE = {Lectures on the geometry of flag varieties},
 BOOKTITLE = {Topics in cohomological studies of algebraic varieties},
    SERIES = {Trends Math.},
     PAGES = {33--85},
 PUBLISHER = {Birkh\"{a}user, Basel},
      YEAR = {2005},
   MRCLASS = {14M15 (14C35 19E08)},
  MRNUMBER = {2143072},
MRREVIEWER = {Christian Ohn},
       DOI = {10.1007/3-7643-7342-3\_2},
}

@article {B09,
    AUTHOR = {Brion, Michel},
     TITLE = {Introduction to actions of algebraic groups},
    SERIES = {Notes of the course ``Actions hamiltoniennes:  invariants et classification'' (CIRM, Luminy, 2009)},
       URL = {https://www-fourier.ujf-grenoble.fr/~mbrion/notes_luminy.pdf},
}

@book {Bump,
    AUTHOR = {Bump, Daniel and Schilling, Anne},
     TITLE = {Crystal bases},
      NOTE = {Representations and combinatorics},
 PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ},
      YEAR = {2017},
     PAGES = {xii+279},
      ISBN = {978-981-4733-44-1},
   MRCLASS = {05-01 (05E10 14T05 17B10)},
  MRNUMBER = {3642318},
       DOI = {10.1142/9876},
}

@misc{CanSaha,
      AUTHOR = {{Bilen Can}, M. and {Saha}, P.},
      EPRINT = {2305.00468},
  EPRINTTYPE = {arxiv},
       TITLE = {Applications of Homogeneous Fiber Bundles to the Schubert Varieties},
        YEAR = {2023}}

@article {DeCon-Lak,
    AUTHOR = {De Concini, C. and Lakshmibai, V.},
     TITLE = {Arithmetic {C}ohen-{M}acaulayness and arithmetic normality for
              {S}chubert varieties},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {103},
      YEAR = {1981},
    NUMBER = {5},
     PAGES = {835--850},
      ISSN = {0002-9327},
   MRCLASS = {14M15 (13H10 14M05)},
  MRNUMBER = {630769},
MRREVIEWER = {H. H. Andersen},
       DOI = {10.2307/2374249},
}

@article {Demazure,
    AUTHOR = {Demazure, Michel},
     TITLE = {D\'{e}singularisation des vari\'{e}t\'{e}s de {S}chubert g\'{e}n\'{e}ralis\'{e}es},
   JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme
              S\'{e}rie},
    VOLUME = {7},
      YEAR = {1974},
     PAGES = {53--88},
      ISSN = {0012-9593},
   MRCLASS = {14M15 (20G05)},
  MRNUMBER = {354697},
MRREVIEWER = {S. I. Gel\cprime fand},
}

@article {FZ02,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {I}. {F}oundations},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {15},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {497--529},
      ISSN = {0894-0347},
   MRCLASS = {16S99 (14M99 17B99)},
  MRNUMBER = {1887642},
MRREVIEWER = {Eric N. Sommers},
       DOI = {10.1090/S0894-0347-01-00385-X},
}

@book {Fulton.Harris,
    AUTHOR = {Fulton, William and Harris, Joe},
     TITLE = {Representation theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {129},
      NOTE = {A first course,
              Readings in Mathematics},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1991},
     PAGES = {xvi+551},
      ISBN = {0-387-97527-6; 0-387-97495-4},
   MRCLASS = {20G05 (17B10 20G20 22E46)},
  MRNUMBER = {1153249},
MRREVIEWER = {James E. Humphreys},
       DOI = {10.1007/978-1-4612-0979-9},
}

@article {GHY,
    AUTHOR = {Gao, Yibo and Hodges, Reuven and Yong, Alexander},
     TITLE = {Classification of {L}evi-spherical {S}chubert varieties},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {29},
      YEAR = {2023},
    NUMBER = {4},
     PAGES = {Paper No. 55, 40},
      ISSN = {1022-1824},
   MRCLASS = {14M27 (05E10 05E14)},
  MRNUMBER = {4615612},
       DOI = {10.1007/s00029-023-00856-9},
}

@article {GHY2,
    AUTHOR = {Gao, Yibo and Hodges, Reuven and Yong, Alexander},
     TITLE = {Classifying {L}evi-spherical {S}chubert varieties},
   JOURNAL = {S\'{e}m. Lothar. Combin.},
  FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire},
    VOLUME = {86B},
      YEAR = {2022},
     PAGES = {Art. 29, 12},
   MRCLASS = {05E14 (14M15 14M27)},
  MRNUMBER = {4490870},
}

@article {Hodges.Lakshmibai,
    AUTHOR = {Hodges, Reuven and Lakshmibai, Venkatramani},
     TITLE = {Levi subgroup actions on {S}chubert varieties, induced
              decompositions of their coordinate rings, and sphericity
              consequences},
   JOURNAL = {Algebr. Represent. Theory},
  FJOURNAL = {Algebras and Representation Theory},
    VOLUME = {21},
      YEAR = {2018},
    NUMBER = {6},
     PAGES = {1219--1249},
      ISSN = {1386-923X},
   MRCLASS = {20G05 (05E10 14L30 14M27 20C33)},
  MRNUMBER = {3874743},
MRREVIEWER = {Vladimir L. Popov},
       DOI = {10.1007/s10468-017-9744-6},
}

@article {Hodges.Yong1,
    AUTHOR = {Hodges, Reuven and Yong, Alexander},
     TITLE = {Coxeter combinatorics and spherical {S}chubert geometry},
   JOURNAL = {J. Lie Theory},
  FJOURNAL = {Journal of Lie Theory},
    VOLUME = {32},
      YEAR = {2022},
    NUMBER = {2},
     PAGES = {447--474},
      ISSN = {0949-5932},
   MRCLASS = {14M15 (05E14 14L30)},
  MRNUMBER = {4394321},
MRREVIEWER = {Subramaniam Senthamarai Kannan},
}


@incollection {Howe,
    AUTHOR = {Howe, Roger},
     TITLE = {Perspectives on invariant theory: {S}chur duality,
              multiplicity-free actions and beyond},
 BOOKTITLE = {The {S}chur lectures (1992) ({T}el {A}viv)},
    SERIES = {Israel Math. Conf. Proc.},
    VOLUME = {8},
     PAGES = {1--182},
 PUBLISHER = {Bar-Ilan Univ., Ramat Gan},
      YEAR = {1995},
   MRCLASS = {13A50 (15A72 20G05 22E46)},
  MRNUMBER = {1321638},
MRREVIEWER = {Frank D. Grosshans},
}

@book {Humphreys,
    AUTHOR = {Humphreys, James E.},
     TITLE = {Linear algebraic groups},
    SERIES = {Graduate Texts in Mathematics, No. 21},
 PUBLISHER = {Springer-Verlag, New York-Heidelberg},
      YEAR = {1975},
     PAGES = {xiv+247},
   MRCLASS = {20GXX (14LXX)},
  MRNUMBER = {396773},
MRREVIEWER = {T. Ono},
}


@book {Humphreys:grey,
    AUTHOR = {Humphreys, James E.},
     TITLE = {Reflection groups and {C}oxeter groups},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {29},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1990},
     PAGES = {xii+204},
      ISBN = {0-521-37510-X},
   MRCLASS = {20-02 (20F32 20F55 20G15 20H15)},
  MRNUMBER = {1066460},
MRREVIEWER = {Louis Solomon},
       DOI = {10.1017/CBO9780511623646},
}

@book {J03,
    AUTHOR = {Jantzen, Jens Carsten},
     TITLE = {Representations of algebraic groups},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {107},
   EDITION = {Second},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2003},
     PAGES = {xiv+576},
      ISBN = {0-8218-3527-0},
   MRCLASS = {20G05 (17B10)},
  MRNUMBER = {2015057},
}


@article {Jos.Normal,
    AUTHOR = {Joseph, A.},
     TITLE = {On the {D}emazure character formula},
   JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme
              S\'{e}rie},
    VOLUME = {18},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {389--419},
      ISSN = {0012-9593},
   MRCLASS = {17B10 (14M15 20G05)},
  MRNUMBER = {826100},
MRREVIEWER = {James E. Humphreys},
}


@article {Karrup,
    AUTHOR = {Karuppuchamy, Paramasamy},
     TITLE = {On {S}chubert varieties},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {41},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {1365--1368},
      ISSN = {0092-7872},
   MRCLASS = {14M15 (14M25)},
  MRNUMBER = {3044412},
MRREVIEWER = {Harry Tamvakis},
       DOI = {10.1080/00927872.2011.635620},
}

@book {LR08,
    AUTHOR = {Lakshmibai, Venkatramani and Raghavan, Komaranapuram N.},
     TITLE = {Standard monomial theory},
    SERIES = {Encyclopaedia of Mathematical Sciences},
    VOLUME = {137},
      NOTE = {Invariant theoretic approach,
              Invariant Theory and Algebraic Transformation Groups, 8},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2008},
     PAGES = {xiv+265},
      ISBN = {978-3-540-76756-5},
   MRCLASS = {14M15 (14L24 14L30 14M12 14M17)},
  MRNUMBER = {2388163},
MRREVIEWER = {Dmitry A. Timash\"{e}v},
}


@article {Littel,
    AUTHOR = {Littelmann, Peter},
     TITLE = {On spherical double cones},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {166},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {142--157},
      ISSN = {0021-8693},
   MRCLASS = {14L30 (13A50 22E46)},
  MRNUMBER = {1276821},
MRREVIEWER = {Frank D. Grosshans},
       DOI = {10.1006/jabr.1994.1145},
}

@incollection {L90,
    AUTHOR = {Lusztig, G.},
     TITLE = {Canonical bases arising from quantized enveloping algebras.
              {II}},
      NOTE = {Common trends in mathematics and quantum field theories
              (Kyoto, 1990)},
   JOURNAL = {Progr. Theoret. Phys. Suppl.},
  FJOURNAL = {Progress of Theoretical Physics. Supplement},
    NUMBER = {102},
      YEAR = {1990},
     PAGES = {175--201 (1991)},
      ISSN = {0375-9687},
   MRCLASS = {17B35},
  MRNUMBER = {1182165},
MRREVIEWER = {Ya. S. So\u{\i}bel\cprime man},
       DOI = {10.1143/PTPS.102.175},
}

@article {MWZ,
    AUTHOR = {Magyar, Peter and Weyman, Jerzy and Zelevinsky, Andrei},
     TITLE = {Multiple flag varieties of finite type},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {141},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {97--118},
      ISSN = {0001-8708},
   MRCLASS = {14M15 (16G20)},
  MRNUMBER = {1667147},
MRREVIEWER = {Michel Brion},
       DOI = {10.1006/aima.1998.1776},
}

@article {MWZ2,
    AUTHOR = {Magyar, Peter and Weyman, Jerzy and Zelevinsky, Andrei},
     TITLE = {Symplectic multiple flag varieties of finite type},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {230},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {245--265},
      ISSN = {0021-8693},
   MRCLASS = {14M15 (14L30 16G20)},
  MRNUMBER = {1774766},
MRREVIEWER = {Dmitri I. Panyushev},
       DOI = {10.1006/jabr.2000.8313},
}

@article {Perrin,
    AUTHOR = {Perrin, Nicolas},
     TITLE = {On the geometry of spherical varieties},
   JOURNAL = {Transform. Groups},
  FJOURNAL = {Transformation Groups},
    VOLUME = {19},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {171--223},
      ISSN = {1083-4362},
   MRCLASS = {14M27 (14-02)},
  MRNUMBER = {3177371},
MRREVIEWER = {Paolo Bravi},
       DOI = {10.1007/s00031-014-9254-0},
}

@article {RR,
    AUTHOR = {Ramanan, S. and Ramanathan, A.},
     TITLE = {Projective normality of flag varieties and {S}chubert
              varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {217--224},
      ISSN = {0020-9910},
   MRCLASS = {14M15 (14E25)},
  MRNUMBER = {778124},
MRREVIEWER = {Konrad Drechsler},
       DOI = {10.1007/BF01388970},
}

@article {STEM,
    AUTHOR = {Stembridge, John R.},
     TITLE = {Multiplicity-free products of {S}chur functions},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {5},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {113--121},
      ISSN = {0218-0006},
   MRCLASS = {05E05 (05E15 20G05)},
  MRNUMBER = {1904379},
MRREVIEWER = {Timothy Y. Chow},
       DOI = {10.1007/s00026-001-8008-6},
}

@article {Stem:Weyl,
    AUTHOR = {Stembridge, John R.},
     TITLE = {Multiplicity-free products and restrictions of {W}eyl
              characters},
   JOURNAL = {Represent. Theory},
  FJOURNAL = {Representation Theory. An Electronic Journal of the American
              Mathematical Society},
    VOLUME = {7},
      YEAR = {2003},
     PAGES = {404--439},
   MRCLASS = {17B10 (05E15 20G05)},
  MRNUMBER = {2017064},
MRREVIEWER = {Hiro-Fumi Yamada},
       DOI = {10.1090/S1088-4165-03-00150-X},
}

@article {VK78,
    AUTHOR = {Vinberg, \`E. B. and Kimel'fel'd, B. N.},
     TITLE = {Homogeneous domains on flag manifolds and spherical subgroups
              of semisimple {L}ie groups},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u{\i} Analiz i ego
              Prilozheniya},
    VOLUME = {12},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {12--19, 96},
      ISSN = {0374-1990},
   MRCLASS = {32M10 (14F05 14L30 14M17 20G05)},
  MRNUMBER = {509380},
MRREVIEWER = {Alan T. Huckleberry},
}