Linear and Shalika local periods for the mirabolic group, and some consequences

2012/10/16 by Matringe, Nadir
#11S40 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1210.4307

Abstract

Using linear periods on the mirabolic subgroup of GL(n,F), for F a non archimedean local field, we give a list of the maximal Levi subgroups of GL(n,F) which can distinguish a discrete series, and a generic representation. We also obtain the functional equation of the local exterior-square L-function of a generic representation of GL(n,F) when n=2m is even. Then we discuss the relation between Shalika models and local models for representations of GL(2m,F). Finally we give a necessary and sufficient condition on the cuspidal representation ρ for a generalised Steinberg representation St_k(ρ) of GL(2m,F) to have a local model.

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