Représentations de Weil et GL₂
Subtitle: algèbres de division et GLn̳ : (vers les corps de classes galoisiens I, II)
By: Tetsuo Kaise.
Series: Lecture notes in mathematics ;; 1252; Lecture notes in mathematics (Springer-Verlag) ;; 1252.
Publisher: Springer-Verlag
Published: 1987
Place of publication: Berlin; New York
Language: fre
Number of pages: 203
Subjects: Representations of algebras.; Weil group.
Description: 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.
Notes: Bibliography: p. 202-203.