Simplicity of the branching of representations of the groups GL$(n,q)$ the parabolic restriction: an elementary proof

E. E. Goryachko

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Simplicity of the branching of representations of the groups GL$(n,q)$ the parabolic restriction: an elementary proof

E. E. Goryachko

Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 82-87

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Résumé

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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     author = {E. E. Goryachko},
     title = {Simplicity of the branching of representations of the groups {GL}$(n,q)$ the parabolic restriction: an elementary proof},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--87},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a7/}
}

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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/