Distinction of some induced representations

Details Distinction of some induced representations Distinction of some induced representations

2008-11-23

arxiv.org/abs/0811.3733v11

Mathematics

Representation Theory

An important mistake in the previous version has been corrected here

Scientific paper

Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient of $\pi$, and by $\pi^{\sigma}$ the representation $\pi\circ \sigma$, we show that the representation of $GL(2n, K)$ obtained by normalized parabolic induction of the representation $\pi^\vee \otimes \pi^\sigma$ 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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