The Combinatorics of GLn Generalized Gelfand–Graev Characters

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Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, generalized Gelfand-Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanka's definition in type A in a way that gives far more computational flexibility. We use these alternate constructions to show how to obtain generalized Gelfand-Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand-Graev characters in terms of unipotent representations, thereby recovering the Kosta-Foulkes polynominals as multiplicities.

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This is the peer reviewed version of the following article:

Andrews, S. &Thiem, N. (2017). The Combinatorics of GLn Generalized Gelfand-Graev-Characters. Journal of the London Mathematical Society, 95(2), 475-499. doi: 10.1112/jlms.12023

which has been published in final form at doi: 10.1112/jlms.12023. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.