The Descent Map from Automorphic Representations of GL(n) to Classical Groups

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World Scientific, 2011 - Algebra - 339 pages
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This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of GelfandOCoGraev type, or of FourierOCoJacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.
 

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Contents

1 Introduction
1
2 On Certain Residual Representations
17
3 Coefficients of GelfandGraev Type of FourierJacobi Type and Descent
41
4 Some double coset decompositions
65
GelfandGraev characters
81
FourierJacobi characters
121
7 The tower property
151
8 Nonvanishing of the descent I
187
9 Nonvanishing of the descent II
235
10 Global genericity of the descent and global integrals
281
11 Langlands weak functorial lift and descent
313
Bibliography
335
Index
339
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