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Abstract: For or , isomorphism classes of irreducible -modules for are parametrized by n-dimensional representations of the Weil group of F. We can induce to a representation of , which has index 2 in . That gives a process of “automorphic induction” which to an irreducible -module τ for associates an irreducible -module for . In the present paper we show that if τ is unitary and generic then π is determined by τ, up to isomorphism, via a character identity entirely analogous to the character identity occurring in the automorphic induction process for p-adic fields. This completes the theory of automorphic induction for local and global representations of over number fields. [Copyright &y& Elsevier]

Abstract: A bounded linear operator on a Hilbert space is said to be reflexive if the operators which leave invariant the invariant subspaces of T are wot-limits of polynomials in T. In this paper we give a necessary and sufficient condition for an extension of a subnormal operator by an algebraic one to be reflexive.We also give a formula for the reflexivity defect of such extensions. [Copyright &y& Elsevier]