Distinction of some induced representations
- Autores: Nadir Matringe
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 1, 2010, págs. 77-98
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n1.a7
- Enlaces
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Resumen
Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\Delta$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\Delta^{\vee}$ the smooth contragredient of $\Delta$, and by $\Delta^{\sigma}$ the representation $\Delta\circ \sigma$, we show that representation of $GL(2n, K)$ obtained by normalized parabolic induction of the representation $\Delta^\vee \otimes \Delta^\sigma$, 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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