Description
Book SynopsisThis 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 Gelfand-Graev type, or of Fourier-Jacobi 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.
Table of ContentsCertain Residual Eisenstein Series; Fourier Coefficients of Gelfand-Graev Type and Fourier-Jacobi Type; Jacquet Modules Corresponding to Gelfand-Graev Models; Jacquet Modules Corresponding to Fourier-Jacobi Models; The Tower Property; Non-Vanishing of the Descent; On the Global Genericity of the Descent and Rankin-Selberg Integrals; The Descent and Langlands Functoriality from Classical Groups to GL(n); Applications of the Descent (Generalized Endoscopy, Base Change).
