Completing an extension of Tunnellʹs theorem Original Research Article

We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π+ of G how does π+ decompose on restriction to H. Here G is GL(2,F)+, where F is a nonarchimedian local field of characteristic not two, K a separable quadratic extension of F, GL(2,F)+ the subgroup of index 2 in GL(2,F) consisting of those matrices whose determinant is in NK/F(K*), π+ is an irreducible, admissible supercuspidal representation of GL(2,F)+ and H=K* under an embedding of K* into GL(2,F).