Strong density of spherical characters attached to unipotent subgroups

2022/02/10 by Aizenbud, Avraham, Bernstein, Joseph, Sayag, Eitan
#20G05 #20G25 #43A85 #46F99 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2202.04984

Abstract

We prove the following result in relative representation theory of a reductive p-adic group G: Let U be the unipotent radical of a minimal parabolic subgroup of G, and let ψ be an arbitrary smooth character of U. Let S ⊂ Irr(G) be a Zariski dense collection of irreducible representations of G. Then the span of the Bessel distributions B_π attached to representations π from S is dense in the space \mathcal S^*(G)^{U× U,ψ× ψ} of all (U× U,ψ× ψ)-equivariant distributions on G. We base our proof on the following results: 1. The category of smooth representations \mathcal M(G) is Cohen-Macaulay. 2. The module ind_U^G(ψ) is a projective module.

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