| Titre : | Smooth-automorphic forms and smooth-automorphic representations |
| Auteurs : | Harald Grobner, Auteur |
| Type de document : | document électronique |
| Editeur : | New Jersey : World Scientific, 2023 |
| ISBN/ISSN/EAN : | 978-981-1246173-- |
| Format : | 1 vol. (262 p.) / ill., couv. ill. en coul |
| Note générale : | Bibliogr.Index |
| Langues: | Français |
| Index. décimale : | 515 (Analyse (mathématique)) |
| Catégories : | |
| Mots-clés: | Automorphic Forms Representation Smooth-Automorphic Form |
| 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. |
| Note de contenu : |
Contents:
* Local Groups: - Basic Notions and Concepts from Functional Analysis ("Local"). - Representations of Local Groups — The Very Basics. - Langlands Classification: Step 1 — What to Classify?. - Langlands Classification: Step 2. - Langlands Classification: Step 3. - Special Representations: Part 1. - Special Representations: Part 2. * Global Groups: - Basic Notions and Concepts from Functional Analysis ("Global"). - First Adelic Steps. - Representations of Global Groups — The Very Basics. - Automorphic Forms and Smooth-Automorphic Forms. - Automorphic Representations and Smooth-Automorphic. - Cuspidality and Square-integrability. - Parabolic Support. - Cuspidal Support. |
| Côte titre : | EB/065 |
| En ligne : | https://www.worldscientific.com/doi/epdf/10.1142/12523 |
Exemplaires (1)
| Cote | Support | Localisation | Disponibilité |
|---|---|---|---|
| EB/065 | Livre | Bibliothèque centrale | Disponible |
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