Comptes Rendus
no. 1
Group theory
Vanishing of local symplectic periods for cuspidal representations of the unitary group
[Nullité des périodes symplectiques locales pour les représentations cuspidales du groupe unitaire]

Présenté par : the Editorial Board

Arnab Mitra1 ; Omer Offen1
1 Department of Mathematics, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 15-19.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.009
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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