Induction automorphe pour GL(n,C)

For F = R or C, isomorphism classes of irreducible (g,K)-modules for GL(n,F) are parametrized by n-dimensional representations of the Weil group WF of F. We can induce to WR a representation of WC, which has index 2 in WR. That gives a process of “automorphic induction” which to an irreducible (g,K)- module τ for GL(n,C) associates an irreducible (g,K)-module π = τC/R for GL(2n,R). 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 GL(n) over number fields. © 2009 Elsevier Inc. Tous droits réservés.