Modular cuspidal representations of GL(n,F) distinguished by a Galois involution

17.05.2022 13:15 - 14:45

Vincent Sécherre (U Versailles)

Let E/F be a separable quadratic extension of p-adic fields. If G=GL(n,E) and H=GL(n,F), the quotient space G/H is a symmetric space, and the study of the representation of G on the vector space of smooth functions on G/H belongs to what is known as the Relative Local Langlands Programme. In particular, one is interested in the irreducible subrepresentations of this vector space, the so-called H-distinguished representations of G. The case of representations with complex coefficients has been widely investigated by various authors. Much less known is the case where representations have coefficients in finite fields, whose characteristic is assumed to be different from p. Distinguished modular supercuspidal representations of G are fairly well understood, and behave essentially as in the complex case, at least when p is not 2. In this talk, I will discuss the case of non-supercuspidal, cuspidal representations. This is a work in progress, joint with Kurinczuk and Matringe.




H. Grobner, A. Minguez-Espallargas, A. Mellit


SR 10, 2. OG., OMP 1