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The Langlands Classification and Irreducible Characters for Real Reductive Groups

  • Jeffrey Adams
  • Dan Barbasch
  • David A. VoganJr.

Part of the Progress in Mathematics book series (PM, volume 104)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 1-27
  3. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 28-40
  4. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 41-46
  5. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 47-54
  6. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 55-63
  7. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 64-81
  8. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 82-97
  9. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 98-104
  10. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 105-112
  11. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 113-119
  12. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 120-138
  13. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 139-146
  14. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 147-156
  15. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 157-166
  16. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 167-174
  17. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 175-188
  18. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 189-204
  19. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 205-211
  20. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 212-221
  21. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 222-233
  22. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 234-238
  23. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 239-247
  24. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 248-251
  25. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 252-265
  26. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 266-274
  27. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 275-294
  28. Jeffrey Adams, Dan Barbasch, David A. Vogan Jr.
    Pages 295-310
  29. Back Matter
    Pages 311-320

About this book

Introduction

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.

Keywords

algebra algebraic group automorphic forms cls field homomorphism representation theory

Authors and affiliations

  • Jeffrey Adams
    • 1
  • Dan Barbasch
    • 2
  • David A. VoganJr.
    • 3
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0383-4
  • Copyright Information Birkhäuser Boston 1992
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6736-2
  • Online ISBN 978-1-4612-0383-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site