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Représentations de Weil et GL2 Algèbres de division et GLn

(Vers les corps de classes galoisiens I, II)

  • Authors
  • Tetsuo Kaise

Part of the Lecture Notes in Mathematics book series (LNM, volume 1252)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Tetsuo Kaise
    Pages 1-98
  3. Tetsuo Kaise
    Pages 99-201
  4. Back Matter
    Pages 202-203

About this book

Introduction

This monograph represents the first two parts of the author's research on the generalization of class field theory for the noncommutative case. Part I concentrates on the construction of all the irreducible representations of a multiplicative group B* of a quaternion algebra B over a local field k with residue field of characteristic 2. These results are of considerable significance in the light of the connections found by Jacquet-Langlands between representations of GL2 (k) and B* and although they concern GL2 they also provide a model for GLn. Part II deals with n 2 unifying results previously obtained by Weil, Jacquet-Langlands, Bernstein-Zelevinskii, Deligne-Kazdan and others. More than a mere comparison of these results, it reveals an intrinsic correspondence found with the aid of the base restriction process of algebraic groups and the substitution of division of algebras for Cartan subalgebras. The approach is purely local and therefore may be applied also to other types of reductive groups, in particular Sp2l as well as to archimedean cases. This book will be of great interest to researchers and graduate students working in algebraic number theory and automorphic forms.

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0077390
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17827-9
  • Online ISBN 978-3-540-47871-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site