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Abstract. In this paper we prove that a unitary representation of Sp(p, q) whose infinitesimal character satisfies some regularity condition is infinitesimally isomorphic to an Aq (λ) module. This is done using similar techniques as those used by the author in earlier work.

Abstract. This paper presents some recent progress on the classification of the unitary genuine irreducible representations of the metaplectic group Mp(2n). Our focus will be on Langlands quotients of genuine minimal principal series; the main result is an embedding of the set of unitary parameters of such representations into the union of spherical unitary parameters for certain split orthogonal groups. The latter are known from work of D. Barbasch; hence we obtain the non-unitarity of a large (conjecturally complete) set of parameters for Langlands quotients of genuine principal series of Mp(2n).

Abstract. We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.