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Représentations de Weil et GL₂ : algèbres de division et GLn̳ : (vers les corps de classes galoisiens I, II)

Author: Tetsuo Kaise
Publisher: Berlin ; New York : Springer-Verlag, ©1987.
Series: Lecture notes in mathematics (Springer-Verlag), 1252.
Edition/Format:   eBook : Document : FrenchView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kaise, Tetsuo.
Représentations de Weil et GL₂.
Berlin ; New York : Springer-Verlag, ©1987
(DLC) 87154717
(OCoLC)16933702
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tetsuo Kaise
ISBN: 9783540478713 354047871X
OCLC Number: 298571578
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (vii, 203 pages).
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: Table des matires: Reprsentation de Weil de GL2 --
Algbres de division et GLn --
Bibliographie.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1252.
Responsibility: Tetsuo Kaise.

Abstract:

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.

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