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- Title
Formules de caractères pour l'induction automorphe.
- Authors
Henniart, Guy; Lemaire, Bertrand
- Abstract
Let E/F be a finite cyclic extension of p-adic fields, of degree d, and let κ be a character of F× with kernel NE/F ( E×). Automorphic induction corresponds, via the Langlands correspondence, to inducing Galois representations from E to F. To a smooth irreducible representation τ of GL m( E) automorphic induction attaches a smooth irreducible representation π of GL md( F) which is equivalent to ( κ ○ det) ⊗ π. When π is generic the relation between τ and π is expressed by saying that a certain character function attached to τ is proportional to another character function attached to π and the choice of an intertwining operator A of ( κ ○ det) ⊗ π onto π. Here we normalize A through Whittaker models so that the proportionality constant—we prove—does not depend on τ. This is used in current work of C. J. Bushnell and the first author to give an explicit description of the Langlands correspondence for cuspidal smooth irreducible representations of GL n( F) when n is prime to p. In the present paper we also give a proof of the fundamental lemma for automorphic induction when p is at most n, thus completing J.-L. Waldspurger's result when p > n.
- Subjects
P-adic fields; AUTOMORPHIC functions; MATHEMATICAL induction; GALOIS theory; FINITE fields; ALGEBRAIC fields
- Publication
Journal für die Reine und Angewandte Mathematik, 2010, Vol 2010, Issue 645, p41
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/CRELLE.2010.059