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arXiv · 0811.3733

Distinction of some induced representations

Nadir Matringe
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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 $π\circ σ$, we show that the representation of $GL(2n, K)$ obtained by normalized parabolic induction of the representation $π^\vee \otimes π^σ$ 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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Nadir Matringe. 2009-10-21. Distinction of some induced representations. https://arxiv.org/abs/0811.3733

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