Residues of standard intertwining operators on p-adic classical groups

Abstract

Abstract We study two basic problems involved in the study of the standard intertwining operators attached to representations induced from irreducible unitary supercuspidal representations on maximal parabolic subgroups of p-adic classical groups. We give a formula to transfer the integrals over the unipotent radical to orbital integrals under the adjoint action of the Levi subgroup, and conclude that the residue of such standard intertwining operators at s = 0 ${s=0}$ is determined by compact orbital integrals.