SUPERCUSPIDAL REPRESENTATIONS OF GL(N) DISTINGUISHED BY A UNITARY SUBGROUP

When E/F is a quadratic extension of p-adic fields, with p not equal 2 , and H' is a unitary similitude group in GL(n, E), it is shown that f or every irreducible supercuspidal representation pi of GL(n, E) of lo west level the space of H'-invariant linear forms has dimension at mos t one. The analogous fact for the corresponding unitary group H is als o considered and the dimension of the space of H-invariant linear form s is computed in terms of the corresponding dimension associated to th e inducing representation.