About The Book
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 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.
Contents
Introduction:
• On Certain Residual Representations:
• Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent:
• Some Double coset decompositions:
• Jacquet modules of parabolic inductions: Gelfand-Graev characters:
• Jacquet modules of parabolic inductions: Fourier-Jacobi characters:
• The Tower property:
• Non-vanishing of the descent I:
• Non-vanishing of the descent II:
• Global genericity of the descent and global integrals: