On the relationship between distinction and irreducibility of parabolic induction

Arnab Mitra

doi:10.1016/j.crma.2019.10.009

Number theory

On the relationship between distinction and irreducibility of parabolic induction

Presented by: the Editorial Board

Arnab Mitra ¹

¹ Indian Institute of Science Education and Research Tirupati, India

Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 827-831.

Abstract
Résumé

Let $U_{2 n}$ denote the quasi-split unitary group over 2n variables with respect to a quadratic extension $E / F$ of p-adic fields. In this short note, we relate ${GL}_{n} (F)$ -distinction of ladder representations of ${GL}_{n} (E)$ with irreducibility of its Siegel parabolic induction in $U_{2 n}$ .

Soit $U_{2 n}$ le groupe unitaire quasi déployé à 2n variables associé à une extension $E / F$ de corps p-adiques. Dans cette courte note, nous établissons un lien entre la propriété de distinction par ${GL}_{n} (F)$ d'une représentation en échelle de ${GL}_{n} (E)$ et l'irréductibilité de son induite parabolique.

Received: 2019-09-12
Accepted: 2019-10-22
Published online: 2019-11-01

DOI: 10.1016/j.crma.2019.10.009

Author's affiliations:

Arnab Mitra ¹

¹ Indian Institute of Science Education and Research Tirupati, India

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Arnab Mitra. On the relationship between distinction and irreducibility of parabolic induction. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 827-831. doi : 10.1016/j.crma.2019.10.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.10.009/

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