Geodesic
Simplicity of the branching of representations of the groups GL$(n,q)$ the parabolic restriction: an elementary proof
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 82-87.

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It is well known that the branching of representations of the groups $\operatorname{GL}(n,q)$ under the parabolic restriction is simple. Apparently, an elementary proof of this important fact has not been found so far. We present such a proof, which uses a method not standard for the representation theory of finite groups.
Keywords: representation of $\operatorname{GL}(n,q)$, simplicity of branching, parabolic restriction. 
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E. E. Goryachko. Simplicity of the branching of representations of the groups GL$(n,q)$ the parabolic restriction: an elementary proof. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 82-87. http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a7/

[1] I. N. Bernshtein, A. V. Zelevinskii, UMN, 31:3 (1976), 5–70 | MR

[2] A. M. Vershik, S. V. Kerov, Funkts. analiz i ego pril., 32:3 (1998), 3–10 | DOI | MR | Zbl

[3] A. M. Vershik, A. Yu. Okunkov, Zap. nauchn. sem. POMI, 307, 2004, 57–98 | MR

[4] E. E. Goryachko, Zap. nauchn. sem. POMI, 331, 2006, 43–59 | MR | Zbl

[5] E. E. Goryachko, Zap. nauchn. sem. POMI, 373, 2009, 124–133 | MR

[6] D. K. Faddeev, Zap. nauchn. sem. LOMI, 46, 1974, 64–88 | MR | Zbl

[7] A. Aizenbud, D. Gourevitch, “Multiplicity free Jacquet modules”, Canad. Math. Bull. (to appear) , arXiv: 0910.3659v1 | MR

[8] I. M. Gelfand, D. A. Kajdan, Lie Groups and Their Representations, Akad. Kiadó, Budapest, 1975, 95–118 | MR

[9] J. A. Green, Trans. Amer. Math. Soc., 80:2 (1955), 402–447 | DOI | MR | Zbl

[10] A. M. Vershik, Asymptotic Combinatorics with Applications to Mathematical Physics, Lecture Notes in Math., 1815, Springer-Verlag, Berlin, 2003, 161–182 | DOI | MR | Zbl

[11] A. M. Vershik, S. V. Kerov, Zap. nauchn. sem. POMI, 344, 2007, 5–36 | MR

[12] A. V. Zelevinsky, Representations of Finite Classical Groups. A Hopf algebra approach, Lecture Notes in Math., 869, Springer-Verlag, Berlin–New York, 1981 | DOI | MR | Zbl