Lecture Notes in Mathematics

Représentations de Weil et GL2 - Algèbres de division et GLn

Vers les corps de classes galoisiens I, II

Authors: Kaise, Tetsuo

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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.

Table of contents (2 chapters)

Table of contents (2 chapters)

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-540-47871-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $46.00
price for USA in USD
  • ISBN 978-3-540-17827-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

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
Series Title
Lecture Notes in Mathematics
Series Volume
1252
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47871-3
DOI
10.1007/BFb0077390
Softcover ISBN
978-3-540-17827-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 204
Topics