We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for E/F a quadratic extension of p-adic fields the associated unitary group G=U(n,n+1) contains a parabolic subgroup P with Levi component L isomorphic to GL_n(E) x U₁(E). Let π be an irreducible supercuspidal representation of L of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation is reducible.

The author wishes to thank Alan Roche from University of Oklahoma, USA for suggesting the problem studied in this work and for many discussions and insights.