The Langlands Classification and Irreducible Characters for Real Reductive Groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1992
|
| Series: | Progress in Mathematics
104 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. In the case of real groups, the predicted parametrizations of representations was proved by Langlands himself. Unfortunately, most of the deeper relations suggested by the p-adic theory (between real representation theory and geometry on the space of real Langlands parameters) are not true. The purposed of this book is to redefine the space of real Langlands parameters so as to recover these relationships; informally, to do "Kazhdan-Lusztig theory on the dual group". The new definitions differ from the classical ones in roughly the same way that Deligne's definition of a Hodge structure differs from the classical one. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms |
| Physical Description: | 1 Online-Ressource (XII, 320 p) |
| ISBN: | 9781461203834 9781461267362 |
| DOI: | 10.1007/978-1-4612-0383-4 |
Staff View
MARC
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| indexdate | 2024-07-10T01:21:05Z |
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| language | English |
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| spelling | Adams, Jeffrey Verfasser aut The Langlands Classification and Irreducible Characters for Real Reductive Groups by Jeffrey Adams, Dan Barbasch, David A. Vogan Boston, MA Birkhäuser Boston 1992 1 Online-Ressource (XII, 320 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 104 This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. In the case of real groups, the predicted parametrizations of representations was proved by Langlands himself. Unfortunately, most of the deeper relations suggested by the p-adic theory (between real representation theory and geometry on the space of real Langlands parameters) are not true. The purposed of this book is to redefine the space of real Langlands parameters so as to recover these relationships; informally, to do "Kazhdan-Lusztig theory on the dual group". The new definitions differ from the classical ones in roughly the same way that Deligne's definition of a Hodge structure differs from the classical one. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms Mathematics Algebra Group theory Group Theory and Generalizations Associative Rings and Algebras Mathematik Unitäre Darstellung (DE-588)4186906-0 gnd rswk-swf Lokale Langlands-Vermutung (DE-588)4211641-7 gnd rswk-swf Reduktive Gruppe (DE-588)4177313-5 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Irreduzible Darstellung (DE-588)4162430-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Langlands-Klassifizierung (DE-588)4211640-5 gnd rswk-swf Reduktive Gruppe (DE-588)4177313-5 s Irreduzible Darstellung (DE-588)4162430-0 s Langlands-Klassifizierung (DE-588)4211640-5 s 1\p DE-604 Unitäre Darstellung (DE-588)4186906-0 s 2\p DE-604 Lokale Langlands-Vermutung (DE-588)4211641-7 s 3\p DE-604 Darstellungstheorie (DE-588)4148816-7 s 4\p DE-604 Algebraische Geometrie (DE-588)4001161-6 s 5\p DE-604 Barbasch, Dan Sonstige oth Vogan, David A. Sonstige oth https://doi.org/10.1007/978-1-4612-0383-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Adams, Jeffrey The Langlands Classification and Irreducible Characters for Real Reductive Groups Mathematics Algebra Group theory Group Theory and Generalizations Associative Rings and Algebras Mathematik Unitäre Darstellung (DE-588)4186906-0 gnd Lokale Langlands-Vermutung (DE-588)4211641-7 gnd Reduktive Gruppe (DE-588)4177313-5 gnd Darstellungstheorie (DE-588)4148816-7 gnd Irreduzible Darstellung (DE-588)4162430-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Langlands-Klassifizierung (DE-588)4211640-5 gnd |
| subject_GND | (DE-588)4186906-0 (DE-588)4211641-7 (DE-588)4177313-5 (DE-588)4148816-7 (DE-588)4162430-0 (DE-588)4001161-6 (DE-588)4211640-5 |
| title | The Langlands Classification and Irreducible Characters for Real Reductive Groups |
| title_auth | The Langlands Classification and Irreducible Characters for Real Reductive Groups |
| title_exact_search | The Langlands Classification and Irreducible Characters for Real Reductive Groups |
| title_full | The Langlands Classification and Irreducible Characters for Real Reductive Groups by Jeffrey Adams, Dan Barbasch, David A. Vogan |
| title_fullStr | The Langlands Classification and Irreducible Characters for Real Reductive Groups by Jeffrey Adams, Dan Barbasch, David A. Vogan |
| title_full_unstemmed | The Langlands Classification and Irreducible Characters for Real Reductive Groups by Jeffrey Adams, Dan Barbasch, David A. Vogan |
| title_short | The Langlands Classification and Irreducible Characters for Real Reductive Groups |
| title_sort | the langlands classification and irreducible characters for real reductive groups |
| topic | Mathematics Algebra Group theory Group Theory and Generalizations Associative Rings and Algebras Mathematik Unitäre Darstellung (DE-588)4186906-0 gnd Lokale Langlands-Vermutung (DE-588)4211641-7 gnd Reduktive Gruppe (DE-588)4177313-5 gnd Darstellungstheorie (DE-588)4148816-7 gnd Irreduzible Darstellung (DE-588)4162430-0 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Langlands-Klassifizierung (DE-588)4211640-5 gnd |
| topic_facet | Mathematics Algebra Group theory Group Theory and Generalizations Associative Rings and Algebras Mathematik Unitäre Darstellung Lokale Langlands-Vermutung Reduktive Gruppe Darstellungstheorie Irreduzible Darstellung Algebraische Geometrie Langlands-Klassifizierung |
| url | https://doi.org/10.1007/978-1-4612-0383-4 |
| work_keys_str_mv | AT adamsjeffrey thelanglandsclassificationandirreduciblecharactersforrealreductivegroups AT barbaschdan thelanglandsclassificationandirreduciblecharactersforrealreductivegroups AT vogandavida thelanglandsclassificationandirreduciblecharactersforrealreductivegroups |