Discrete series of classical groups

Let G(n) be the split classical groups Sp(2n), SO(2n + 1) and SO(2n) define d over a p-adic field F or the quasi-split classical groups U(n, n) and U(n + 1, n) with respect to a quadratic extension E/F. We prove the self-duali ty of unitary supercuspidal data of standard Levi subgroups of G(n)(F) whic h give discrete series representations of G(n)(F).