Representation Theory and Noncommutative Geometry, Paris

Cuspidal l-modular representations of p-adic GL(n) distinguished by a Galois involution

6 mars 2025, 14:00

1h

Amphitheater Darboux (IHP)

Orateur

vincent secherre (Université de Versailles St-Quentin)

Description

Let $E/F$ be a quadratic extension of $p$-adic fields. A smooth representation of ${\mathrm{G}\mathrm{L}}_n(E)$ is said to be distinguished by ${\mathrm{G}\mathrm{L}}_n(F)$ if it carries a non-zero ${\mathrm{G}\mathrm{L}}_n(F)$-invariant linear form. Distinguished complex representations have been extensively studied: there is in particular a full classification of distinguished generic complex representations. The case of $l$-modular representations (that is, with coefficients in a field whose characteristic is a prime number $l$ different from $p$) is much less well understood. In this talk, I will discuss the case of cuspidal $l$-modular representations (for $p$ odd). This is a joint work with Robert Kurinczuk and Nadir Matringe.