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Mat. Sb., 2014, Volume 205, Number 9, Pages 3–48 (Mi msb8322)  

This article is cited in 7 scientific papers (total in 7 papers)

Spherical actions on flag varieties

R. S. Avdeevab*, A. V. Petukhovc

a Moscow Institute of Open Education
b National Research University "Higher School of Economics", Moscow
c A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: For every finite-dimensional vector space $V$ and every $V$-flag variety $X$ we list all connected reductive subgroups in $\mathrm{GL}(V)$ acting spherically on $X$.
Bibliography: 28 titles.

Keywords: algebraic group, flag variety, spherical variety, nilpotent orbit.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00704
Deutsche Forschungsgemeinschaft SFB701
Mathematisches Forschungsinstitut Oberwolfach
Dynasty Foundation
Max-Planck-Institut für Mathematik

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8322

Full text: PDF file (849 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:9, 1223–1263

Bibliographic databases:

UDC: 512.745
MSC: 14M15, 14M27
Received: 05.01.2014 and 21.06.2014

Citation: R. S. Avdeev, A. V. Petukhov, “Spherical actions on flag varieties”, Mat. Sb., 205:9 (2014), 3–48; Sb. Math., 205:9 (2014), 1223–1263

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8322
  • http://mi.mathnet.ru/eng/msb/v205/i9/p3

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

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    This publication is cited in the following articles:
    1. Avdeev R., Petukhov A., “Spherical Actions on Isotropic Flag Varieties and Related Branching Rules”, Transform. Groups  crossref  mathscinet  isi
    2. M. van Pruijssen, “Multiplicity free induced representations and orthogonal polynomials”, Int. Math. Res. Notices, 2018, no. 7, 2208–2239  crossref  mathscinet  zmath  isi  scopus
    3. M. B. Can, “The cross-section of a spherical double cone”, Adv. Appl. Math., 101 (2018), 215–231  crossref  mathscinet  zmath  isi  scopus
    4. A. Petukhov, “On annihilators of bounded $(\mathfrak{g},\mathfrak{k})$-modules”, J. Lie Theory, 28:4 (2018), 1137–1147  mathscinet  zmath  isi
    5. M. B. Can, R. Hodges, V. Lakshmibai, “Toroidal schubert varieties”, Algebr. Represent. Theory, 23:5 (2020), 1927–1943  crossref  mathscinet  zmath  isi
    6. R. Avdeev, A. Petukhov, “Branching rules related to spherical actions on flag varieties”, Algebr. Represent. Theory, 23:3 (2020), 541–581  crossref  mathscinet  zmath  isi
    7. I D. Panyushev , O. S. Yakimova, “Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties”, Math. Z., 295:1-2 (2020), 101–127  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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