The simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions
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We present a direct proof of the simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions. The proof consists of three steps. First, we reduce the problem to the statement that a certain pair of finite groups is a Gelfand pair. Then, we obtain a criterion for establishing this fact, which generalizes the classical Gelfand’s criterion. Finally, we check the obtained criterion with the help of some matrix computations. Bibliography: 7 titles.
KeywordsRussia Finite Group Direct Proof Mathematical Institute Matrix Computation
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