Smooth-Automorphic Forms & Smooth-Automorphic Representation

By Harald Grobner

This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.

Our approach to automorphic representations differs from the usual literature: We do not consider "K-finite" automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of "smooth-automorphic forms" is intrinsic to the group scheme G/F.

This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.

Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.

• Format: Hardcover
• Language: English
• ISBN: 9811246165
• ISBN13: 9789811246166
• Release Date: June 2023
• Publisher: World Scientific Publishing Company
• Length: 264 Pages
• Weight: 1.15 lbs.
• Dimensions: 0.6" x 6.0" x 9.0"