Distinction of some induced representations

2008/11/23 by Matringe, Nadir
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0811.3733

Abstract

Let K/F be a quadratic extension of p-adic fields, σ the nontrivial element of the Galois group of K over F, and π a quasi-square-integrable representation of GL(n,K). Denoting by π^\vee the smooth contragredient of π, and by π^σ the representation π∘ σ, we show that the representation of GL(2n, K) obtained by normalized parabolic induction of the representation π^\vee ⊗ π^σ is distinguished with respect to GL(2n,F). This is a step towards the classification of distinguished generic representations of general linear groups over p-adic fields.

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