DEGENERATE PRINCIPAL SERIES REPRESENTATIONS FOR U(N,N)

For a quadratic extension E/F of a nonarchimedean local field of chara cteristic other than 2, let G = U(n, n) be the quasisplit unitary grou p of rank n, and let P be the maximal parabolic subgroup of G which st a- bilizes a maximal isotropic subspace. Then P has a Levi decompositi on P = MN with M similar or equal to GL(n, E). In this paper, the poin ts of reducibility and composition series of the degenerate principal series I-n(s, chi) defined by characters of M are determined completel y. The constituents arising as theta lifts of characters of U(m)'s are identified and their behavior under the intertwining operator Mts, ch i): I-n(s, chi) --> I-n(-s, <(chi)over tilde>) is described. The case E = F + F and G similar or equal to GL(2n, F) is included.