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Shintani lifting and Gelfand-Graev representations. (English) Zbl 0654.20046

Representations of finite groups, Proc. Conf., Arcata/Calif. 1986, Pt. 1, Proc. Symp. Pure Math. 47, 147-163 (1987).
[For the entire collection see Zbl 0627.00009.]
The purpose of this paper is to introduce the reader to two topics - Shintani lifting and generalized Gelfand-Graev representations - in the representation theory of finite reductive groups. Although both are meaningful (and perhaps more interesting) for reductive groups over local fields, we almost always confine ourselves to the finite field case; the main exception to this is the last subsection, where we state some conjectures concerning generalized Gelfand-Graev representations of reductive groups over local fields.

MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields

Citations:

Zbl 0627.00009