Représentations de Weil et GL2 - Algèbres de division et GLn : Vers les corps de classes galoisiens I, II. 1st ed. 1987

種類:

電子ブック

責任表示:

by Tetsuo Kaise

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1987

著者名:

• Kaise, Tetsuo.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1252

ISBN:

9783540478713 [354047871X]    

注記:

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 particu

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