Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Andrews Scott

The generalized Gelfand–Graev characters of GLn(Fq)
Scott Andrews  1  , Nathaniel Thiem  2  
1 : Boise State University
1910 University Drive, Boise, Idaho 83725 -  États-Unis
2 : University of Colorado Boulder [Boulder]  -  Website
Boulder, Colorado 80309 -  États-Unis

Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized 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 Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. 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 Kostka–Foulkes polynomials as multiplicities. 

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