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.
\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:
Eric Marberg, Yifeng Zhang, “Perfect models for finite Coxeter groups”, Journal of Pure and Applied Algebra, 227:5 (2023), 107303
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
José O. Araujo, Tim Bratten, “Gelfand models for classical Weyl groups”, Journal of Algebra, 403 (2014), 154
T. Shoji, K. Sorlin, “Exotic symmetric space over a finite field, I”, Transformation Groups, 2013
José O. Araujo, Luis C. Maiarú, Mauro Natale, “A Gelfand Model for Weyl Groups of Type D2n”, ISRN Algebra, 2012 (2012), 1
Marberg E., “Generalized Involution Models for Wreath Products”, Isr. J. Math., 192:1 (2012), 157–195
Caselli F., Fulci R., “Gelfand Models and Robinson-Schensted Correspondence”, J. Algebr. Comb., 36:2 (2012), 175–207
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
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
Lansky J.M., Vinroot C.R., “Klyachko Models of P-Adic Special Linear Groups”, Proc. Amer. Math. Soc., 139:6 (2011), 2271–2279
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
Caselli F., “Involutory Reflection Groups and their Models”, J. Algebra, 324:3 (2010), 370–393
Vinroot C.R., “Character Degree Sums and Real Representations of Finite Classical Groups of Odd Characteristic”, J. Algebra. Appl., 9:4 (2010), 633–658
Garge Sh.M., Oesterle J., “On Gelfand Models for Finite Coxeter Groups”, J. Group Theory, 13:3 (2010), 429–439
J. O. Araujo, J. J. Bigeón, “A Gel'fand Model for the Symmetric Generalized Group”, Communications in Algebra, 37:5 (2009), 1808
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
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
Thiem N., Vinroot C.R., “Values of Character Sums for Finite Unitary Groups”, J. Algebra, 320:3 (2008), 1150–1173
Adin R.M., Postnikov A., Roichman Yu., “Combinatorial Gelfand Models”, J. Algebra, 320:3 (2008), 1311–1325
Offen O., Sayag E., “Uniqueness and Disjointness of Klyachko Models”, J. Funct. Anal., 254:11 (2008), 2846–2865