Distinguished cuspidal representations of GL(2) over a p-adic field

Vincent Sécherre, Institut de Mathématiques de Luminy, Université de la Méditerranée.

(This talk is related to Delorme's course on p-adic symmetric spaces.)

Let F be a p-adic field, and let s be a F-rational involution on GL(2). We address the question of classifying irreducible representations of GL(2,F) which are distinguished by the subgroup of s-fixed point of GL(2,F). Cuspidal representations of GL(2,F) can be constructed by compact induction of an irreducible representation of a compact mod centre subgroup, via the Bushnell-Kutzko theory of simple types. We discuss the distinguishability of such representations in terms of the simple types they contain.