SMOOTH-AUTOMORPHIC FORMS & SMOOTH-AUTOMORPHIC REPRESENTATION - Grobner Harald

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Résumé :
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....