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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

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Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2010, Issue 645

Issues

Formules de caractères pour l'induction automorphe

Guy Henniart
  • Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, CNRS, 91405 Orsay Cedex, France. e-mail :
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Bertrand Lemaire
  • Institut de Mathématiques de Luminy et UMR 6206 du CNRS, Université Aix-Marseille II, Case Postale 907, 163 Av. de Luminy, 13288 Marseille Cedex 9, France. e-mail :
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-08-11 | DOI: https://doi.org/10.1515/crelle.2010.059

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 GLm(E) automorphic induction attaches a smooth irreducible representation π of GLmd(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 GLn(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.

About the article

Received: 2009-03-20

Published Online: 2010-08-11

Published in Print: 2010-08-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2010, Issue 645, Pages 41–84, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2010.059.

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