American Journal of Mathematics

Let G be Sp(2n, F) (resp. SO(2n + 1,F)), where F is a p-adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation π of G an m-tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of π. We show that this correspondence respects the induction and Jacquet module functors (in a sense to be made precise), as well as verifying a number of other useful properties. In essence, this correspondence allows one to isolate the effects of the different families of supercuspidal representations of general linear groups which appear in the support of π.