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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.

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  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    E. E. Goryahko

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  1. E. E. Goryahko
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Correspondence to E. E. Goryahko.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 124–133.

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Goryahko, E.E. The simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions. J Math Sci 168, 379–384 (2010). https://doi.org/10.1007/s10958-010-9989-7

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  • DOI: https://doi.org/10.1007/s10958-010-9989-7

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