Vanishing of local symplectic periods for cuspidal representations of the unitary group

Arnab Mitra; Omer Offen

doi:10.1016/j.crma.2016.11.009

Group theory

Vanishing of local symplectic periods for cuspidal representations of the unitary group

Presented by: the Editorial Board

Arnab Mitra ¹; Omer Offen ¹

¹ Department of Mathematics, Technion – Israel Institute of Technology, Haifa 3200003, Israel

Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 15-19.

Abstract
Résumé

We show that, for a quadratic extension of p-adic fields, no cuspidal representation of the quasi-split unitary group admits a non-trivial linear form invariant by the symplectic subgroup. Our proof is purely local.

Nous montrons que, pour une extension quadratique de corps p-adiques, aucune représentation cuspidale du groupe unitaire semi-déployé n'admet de forme linéaire non nulle invariante par l'action du sous-groupe symplectique. Notre preuve est purement locale.

Received: 2016-09-28
Accepted: 2016-11-24
Published online: 2016-12-07

DOI: 10.1016/j.crma.2016.11.009

Author's affiliations:

Arnab Mitra ¹; Omer Offen ¹

¹ Department of Mathematics, Technion – Israel Institute of Technology, Haifa 3200003, Israel

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Arnab Mitra; Omer Offen. Vanishing of local symplectic periods for cuspidal representations of the unitary group. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 15-19. doi : 10.1016/j.crma.2016.11.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.009/

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