Signs of self-dual depth-zero supercuspidal representations

2016/10/13 by Mishra, Manish
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.04149

Abstract

Let G be a quasi-split tamely ramified connected reductive group defined over a p-adic field F. We show that if -1 is in the F-points of the absolute Weyl group of G, then self-dual supercuspidal representations of G(F) exist. Now assume further that G is unramified and that the center of G is connected. Let π be a generic self-dual depth-zero regular supercuspidal representation of G(F). We show that the Frobenius-Schur indicator of π is given by the sign by which a certain distinguished element of the center of G(F) of order two acts on π.

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