Séminaire Lotharingien de Combinatoire, 80B.24 (2018), 12 pp.

Scott Andrews

The Unipotent Modules of GLn(Fq) via Tableaux

Abstract. We construct the irreducible unipotent modules of the finite general linear groups from actions on tableaux. Our approach is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. We show that our modules are isomorphic to those previously constructed by James (1984), although the two presentations are quite different. Key to our construction are the generalized Gelfand-Graev representations of Kawanaka (1983).

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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