In this paper, we present a proof of the Langlands classification of the irreducible admissible representations of reductive p-adic groups. Then we deduce certain irreducibility results for parabolically induced modules from discrete series representations.

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Abstract. The Howe duality correspondence for a unitary dual pair over R is usually formulated for the determinant cover of the dual pair. For applications to automorphic theory, one has to use the Weil representation of the unitary dual pair (not of the coverings) instead, which is constructed by the doubling argument of Harris et al (Theta dichotomy for unitary groups.