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Mathematics of the USSR-Sbornik, 1984, Volume 48, Issue 2, Pages 365–379
DOI: https://doi.org/10.1070/SM1984v048n02ABEH002680
(Mi sm2136)
 

This article is cited in 44 scientific papers (total in 44 papers)

Models for the complex representations of the groups GL(n,q)

A. A. Klyachko
References:
Abstract: The main result of the paper consists in the construction of a model of the full linear group over a finite field, i.e. its representations such that each irreducible representation occurs as a component precisely once. The series of representations thus constructed has the well-known Gel'fand–Graev representation as first term.
Bibliography: 12 titles.
Received: 01.06.1981
Bibliographic databases:
UDC: 512.7
MSC: 20G40
Language: English
Original paper language: Russian
Citation: A. A. Klyachko, “Models for the complex representations of the groups GL(n,q)”, Math. USSR-Sb., 48:2 (1984), 365–379
Citation in format AMSBIB
\Bibitem{Kly83}
\by A.~A.~Klyachko
\paper Models for the complex representations of the groups~$\operatorname{GL}(n,q)$
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 365--379
\mathnet{http://mi.mathnet.ru/eng/sm2136}
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002680}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=691984}
\zmath{https://zbmath.org/?q=an:0543.20026}
Linking options:
  • https://www.mathnet.ru/eng/sm2136
  • https://doi.org/10.1070/SM1984v048n02ABEH002680
  • https://www.mathnet.ru/eng/sm/v162/i3/p371
  • This publication is cited in the following 44 articles:
    1. Eric Marberg, Yifeng Zhang, “Perfect models for finite Coxeter groups”, Journal of Pure and Applied Algebra, 227:5 (2023), 107303  crossref
    2. Ceccherini-Silberstein T., Scarabotti F., Tolli F., “Mackey's Theory of Tau-Conjugate Representations For Finite Groups”, Jap. J. Math., 10:1 (2015), 43–96  crossref  mathscinet  zmath  isi
    3. José O. Araujo, Tim Bratten, “Gelfand models for classical Weyl groups”, Journal of Algebra, 403 (2014), 154  crossref  mathscinet  zmath
    4. T. Shoji, K. Sorlin, “Exotic symmetric space over a finite field, I”, Transformation Groups, 2013  crossref  mathscinet
    5. José O. Araujo, Luis C. Maiarú, Mauro Natale, “A Gelfand Model for Weyl Groups of Type D2n”, ISRN Algebra, 2012 (2012), 1  crossref  mathscinet
    6. Marberg E., “Generalized Involution Models for Wreath Products”, Isr. J. Math., 192:1 (2012), 157–195  crossref  mathscinet  zmath  isi
    7. Caselli F., Fulci R., “Gelfand Models and Robinson-Schensted Correspondence”, J. Algebr. Comb., 36:2 (2012), 175–207  crossref  mathscinet  zmath  isi
    8. Gourevitch D., Offen O., Sahi S., Sayag E., “Existence of Klyachko Models for Gl(N, R) and Gl(N, C)”, J. Funct. Anal., 262:8 (2012), 3585–3601  crossref  mathscinet  zmath  isi
    9. Aizenbud A., Offen O., Sayag E., “Disjoint Pairs for Gl(N)(R) and Gl(N)(C)”, C. R. Math., 350:1-2 (2012), 9–11  crossref  mathscinet  zmath  isi
    10. Lansky J.M., Vinroot C.R., “Klyachko Models of P-Adic Special Linear Groups”, Proc. Amer. Math. Soc., 139:6 (2011), 2271–2279  crossref  mathscinet  zmath  isi
    11. Murnaghan F., “Regularity and Distinction of Supercuspidal Representations”, Harmonic Analysis on Reductive, P-Adic Groups, Contemporary Mathematics, 543, eds. Doran R., Sally P., Spice L., Amer Mathematical Soc, 2011, 155–183  crossref  mathscinet  zmath  isi
    12. Caselli F., “Involutory Reflection Groups and their Models”, J. Algebra, 324:3 (2010), 370–393  crossref  mathscinet  zmath  isi
    13. Vinroot C.R., “Character Degree Sums and Real Representations of Finite Classical Groups of Odd Characteristic”, J. Algebra. Appl., 9:4 (2010), 633–658  crossref  mathscinet  zmath  isi
    14. Garge Sh.M., Oesterle J., “On Gelfand Models for Finite Coxeter Groups”, J. Group Theory, 13:3 (2010), 429–439  crossref  mathscinet  zmath  isi
    15. J. O. Araujo, J. J. Bigeón, “A Gel'fand Model for the Symmetric Generalized Group”, Communications in Algebra, 37:5 (2009), 1808  crossref  mathscinet  zmath
    16. Nien Ch., “Klyachko Models for General Linear Groups of Rank 5 Over a P-Adic Field”, Can. J. Math.-J. Can. Math., 61:1 (2009), 222–240  crossref  mathscinet  zmath  isi
    17. S. Chaturvedi, G. Marmo, N. Mukunda, R. Simon, “Schwinger representation for the symmetric group: Two explicit constructions for the carrier space”, Physics Letters A, 372:21 (2008), 3763  crossref  mathscinet  zmath  elib
    18. Thiem N., Vinroot C.R., “Values of Character Sums for Finite Unitary Groups”, J. Algebra, 320:3 (2008), 1150–1173  crossref  mathscinet  zmath  isi
    19. Adin R.M., Postnikov A., Roichman Yu., “Combinatorial Gelfand Models”, J. Algebra, 320:3 (2008), 1311–1325  crossref  mathscinet  zmath  isi
    20. Offen O., Sayag E., “Uniqueness and Disjointness of Klyachko Models”, J. Funct. Anal., 254:11 (2008), 2846–2865  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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