RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, Pages 3–26 (Mi izv4091)  

This article is cited in 8 scientific papers (total in 8 papers)

Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups

R. S. Avdeev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The extended weight semigroup of a homogeneous space $G/H$ of a connected semisimple algebraic group $G$ characterizes the spectra of the representations of $G$ on spaces of regular sections of homogeneous line bundles over $G/H$, including the space of regular functions on $G/H$. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces $G/H$, where $G$ is a simply connected non-simple semisimple complex algebraic group and $H$ is a connected closed subgroup of $G$. In all cases we also find the highest-weight functions corresponding to the indecomposable elements of this semigroup. Among other things, our results complete the computation of the weight semigroups for all strictly irreducible simply connected affine spherical homogeneous spaces of semisimple complex algebraic groups.

Keywords: algebraic group, representation, homogeneous space, algebra of invariants, semigroup.

DOI: https://doi.org/10.4213/im4091

Full text: PDF file (654 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:6, 1103–1126

Bibliographic databases:

UDC: 512.745+512.816.4
MSC: 14M27, 22E46, 43A85
Received: 18.02.2009

Citation: R. S. Avdeev, “Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups”, Izv. RAN. Ser. Mat., 74:6 (2010), 3–26; Izv. Math., 74:6 (2010), 1103–1126

Citation in format AMSBIB
\Bibitem{Avd10}
\by R.~S.~Avdeev
\paper Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups
\jour Izv. RAN. Ser. Mat.
\yr 2010
\vol 74
\issue 6
\pages 3--26
\mathnet{http://mi.mathnet.ru/izv4091}
\crossref{https://doi.org/10.4213/im4091}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2779106}
\zmath{https://zbmath.org/?q=an:1209.14039}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010IzMat..74.1103A}
\elib{http://elibrary.ru/item.asp?id=20358768}
\transl
\jour Izv. Math.
\yr 2010
\vol 74
\issue 6
\pages 1103--1126
\crossref{https://doi.org/10.1070/IM2010v074n06ABEH002518}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000287279100001}
\elib{http://elibrary.ru/item.asp?id=16975024}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78651365983}


Linking options:
  • http://mi.mathnet.ru/eng/izv4091
  • https://doi.org/10.4213/im4091
  • http://mi.mathnet.ru/eng/izv/v74/i6/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. N. E. Gorfinkel, “Harmonic Analysis on a Class of Spherical Homogeneous Spaces”, Math. Notes, 90:5 (2011), 678–685  mathnet  crossref  crossref  mathscinet  isi
    2. R. S. Avdeev, “Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup”, Sb. Math., 203:11 (2012), 1535–1552  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. R. S. Avdeev, N. E. Gorfinkel, “Harmonic Analysis on Spherical Homogeneous Spaces with Solvable Stabilizer”, Funct. Anal. Appl., 46:3 (2012), 161–172  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Gindikin S., Goodman R., “Restricted Roots and Restricted Form of the Weyl Dimension Formula for Spherical Varieties”, J. Lie Theory, 23:1 (2013), 257–311  mathscinet  zmath  isi  elib
    5. Avdeev R., “Strongly Solvable Spherical Subgroups and Their Combinatorial Invariants”, Sel. Math.-New Ser., 21:3 (2015), 931–993  crossref  mathscinet  zmath  isi  elib
    6. Bravi P., Pezzini G., “the Spherical Systems of the Wonderful Reductive Subgroups”, J. Lie Theory, 25:1 (2015), 105–123  mathscinet  zmath  isi
    7. Paulus K., Pezzini G., Van Steirteghem B., “On Some Families of Smooth Affine Spherical Varieties of Full Rank”, Acta. Math. Sin.-English Ser., 34:3 (2018), 563–596  crossref  mathscinet  zmath  isi
    8. van Pruijssen M., “Multiplicity Free Induced Representations and Orthogonal Polynomials”, Int. Math. Res. Notices, 2018, no. 7, 2208–2239  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:566
    Full text:72
    References:21
    First page:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019