Skip to main content
  • Book
  • © 1987

Représentations de Weil et GL2 - Algèbres de division et GLn

Vers les corps de classes galoisiens I, II

Authors:

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

  • 404 Accesses

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (2 chapters)

  1. Front Matter

    Pages I-VII
  2. Représentations de Weil de GL2

    • Tetsuo Kaise
    Pages 1-98
  3. Algèbres de division et GLn

    • Tetsuo Kaise
    Pages 99-201
  4. Back Matter

    Pages 202-203

About this book

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

  • Book Title: Représentations de Weil et GL2 - Algèbres de division et GLn

  • Book Subtitle: Vers les corps de classes galoisiens I, II

  • Authors: Tetsuo Kaise

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0077390

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-17827-9Published: 06 May 1987

  • eBook ISBN: 978-3-540-47871-3Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 204

  • Topics: Number Theory

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions