Speaker
vincent secherre
(Université de Versailles St-Quentin)
Description
Let $E/F$ be a quadratic extension of $p$-adic fields. A smooth representation of ${\rm GL}_n(E)$ is said to be distinguished by ${\rm GL}_n(F)$ if it carries a non-zero ${\rm GL}_n(F)$-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.