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Vincent Sécherre, Université de Versailles Saint-Quentin

Description: Number Theory Seminar

Speaker: Vincent Sécherre, Université de Versailles Saint-Quentin

Date & Time: Tuesday, January 30, 14:30-15:30.

Venue: Ramanujan Hall

Title: Supercuspidal representations of GL(n,K) distinguished by GL(n,F),
with K/F a quadratic extension of p-adic fields.

Abstract: Let p be an odd prime number and K/F be a quadratic extension of
p-adic fields. Say that an irreducible representation of GL(n,K) is
distinguished by GL(n,F) if its vector space carries a GL(n,F)-invariant
nonzero linear form. Any distinguished representation is isomorphic to the
contragredient of its Gal(K/F)-conjugate, but the converse is not true. We
will explain how to canonically associate to any
Gal(K/F)-selfcontragredient supercuspidal representation of GL(n,K) a
finite tamely ramified extension T of F and a character of the
multiplicative group of T, by using Bushnell-Kutzko’s theory of types, and
how to get a necessary and sufficient condition on this character for this
supercuspidal representation to be distinguished.
Location: Ramanujan Hall
Date: Tuesday, January 30, 2018
Time: 2:30pm-3:30pm IST
Duration: 1 hour
Access: Public