J. Hakim et Zy. Mao, SUPERCUSPIDAL REPRESENTATIONS OF GL(N) DISTINGUISHED BY A UNITARY SUBGROUP, Pacific journal of mathematics, 185(1), 1998, pp. 149-162
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.