Residues of Intertwining Operators for U(3,3) and Base Change

Abstract

Abstract Let F be a p-adic local field with characteristic 0 and E/F a quadratic extension. Let σ=πG⊗πH be a supercuspidal representation of GL2(E)×UE/F(1,1) with πG conjugate self-dual. In this paper, we use a local approach developed by Shahidi to study the residue of the standard intertwining operator on the parabolic induced representation from σ to the quasi-split unitary group UE/F(3,3) at s=0, and show that if πG is a standard base change from UE/F(1,1), then the residue at s=0 is nonzero if and only if πG is the standard base change of πH.