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Catalogue Information
Field name
Details
Dewey Class
512.2
Title
The Langlands Classification and Irreducible Characters for Real Reductive Groups ([EBook]) / by Jeffrey Adams, Dan Barbasch, David A. Vogan.
Author
Adams, Jeffrey
Added Personal Name
Barbasch, Dan
Vogan, David A.
Other name(s)
SpringerLink (Online service)
Publication
Boston, MA : Birkhäuser , 1992.
Physical Details
XII, 320 pages : online resource.
Series
Progress in mathematics
0743-1643 ; ; 104
ISBN
9781461203834
Summary Note
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.:
Contents note
1. Introduction -- 2. Structure theory: real forms -- 3. Structure theory: extended groups and Whittaker models -- 4. Structure theory: L-groups -- 5. Langlands parameters and L-homomorphisms -- 6. Geometric parameters -- 7. Complete geometric parameters and perverse sheaves -- 8. Perverse sheaves on the geometric parameter space -- 9. The Langlands classification for tori -- 10. Covering groups and projective representations -- 11. The Langlands classification without L-groups -- 12. Langlands parameters and Cartan subgroups -- 13. Pairings between Cartan subgroups and the proof of Theorem 10.4 -- 14. Proof of Propositions 13.6 and 13.8 -- 15. Multiplicity formulas for representations -- 16. The translation principle, the Kazhdan-Lusztig algorithm, and Theorem 1.24 -- 17. Proof of Theorems 16.22 and 16.24 -- 18. Strongly stable characters and Theorem 1.29 -- 19. Characteristic cycles, micro-packets, and Corollary 1.32 -- 20. Characteristic cycles and Harish-Chandra modules -- 21. The classification theorem and Harish-Chandra modules for the dual group -- 22. Arthur parameters -- 23. Local geometry of constructible sheaves -- 24. Microlocal geometry of perverse sheaves -- 25. A fixed point formula -- 26. Endoscopic lifting -- 27. Special unipotent representations -- References.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4612-0383-4
Links to Related Works
Subject References:
Algebra
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Associative rings
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Associative Rings and Algebras
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Group theory
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Group Theory and Generalizations
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Representations of groups
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Rings (Algebra)
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Authors:
Adams, Jeffrey
.
author
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Barbasch, Dan
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Vogan, David A.
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Progress in mathematics
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Classification:
512.2
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