Abstract
Let F a nonarchimedean local field, π, ρ admissible irreducible representations of GL_n (F ), GL_{n−1} (F) respectively. Aizenbud, Gourvitch, Rallis and Schiffmann have recently proved that the space of Hom_{GL_{n−1} (F)} (π, ρ) is at most 1-dimensional and by the works of Waldspurger and Moeglin such dimension is related to a local factor of the couple (π, ρ). In the case n = 2 this phenomenon is known by the works of Tunnell and Saito. In this paper we describe the restriction to Cartan subgroups of irreducible mod p representations π of GL2 (Qp ). In particular we deduce a mod p multiplicity theorem, giving the dimension of Hom_{L×} (π, χ) where L/Qp is a quadratic extension and χ a smooth character of L× .