Representation Theory of Reductive Groups

1. Front Matter

   Pages i-xi

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2. Multipliers and a Paley-Wiener Theorem for Real Reductive Groups

   • James Arthur

   Pages 1-19

3. Weyl Group Representations and Nilpotent Orbits

   • Dan Barbasch, David Vogan

   Pages 21-33

4. A Generalization of Casselman’s Submodule Theorem

   • Alexander Beilinson, Joseph Bernstein

   Pages 35-52

5. Fourier Transforms of Orbits of the Coadjoint Representation

   • Nicole Berline, Michele Vergne

   Pages 53-67

6. IL2 — Cohomology for Groups of Real Rank One

   • W. Casselman

   Pages 69-84

7. Character Relations between Singular Holomorphic Representations

   • Heather Willow Chang

   Pages 85-96

8. A Classification of Unitary Highest Weight Modules

   • Thomas Enright, Roger Howe, Nolan Wallach

   Pages 97-143

9. The Range of the Radon Transform on a Symmetric Space

   • Sigurdur Helgason

   Pages 145-151

10. Weighted Orbital Integrals

    • Rebecca A. Herb

    Pages 153-158

11. Reciprocity Laws in the Theory of Dual Pairs

    • Roger Howe

    Pages 159-175

12. Characters of the Discrete Series for Pseudo-Riemannian Symmetric Spaces

    • Thongchai Kengmana

    Pages 177-183

13. All Supercuspidal Representations of SLℓ over a P-Adic Field are Induced

    • P. C. Kutzko, P. J. Sally Jr.

    Pages 185-196

14. A Note on Invariant Forms on Locally Symmetric Spaces

    • Birgit Speh

    Pages 197-206

15. Oscillatory Integrals and their Applications to Harmonic Analysis on Semisimple Lie Groups

    • V. S. Varadarajan

    Pages 207-222

16. The Kazhdan-Lusztig Conjecture for Real Reductive Groups

    • David A. Vogan Jr.

    Pages 223-264

17. Completeness of Poincaré Series for Automorphic Forms Associated to the Integrable Discrete Series

    • Nolan R. Wallach, Joseph A. Wolf

    Pages 265-281

18. Geometric Methods in Representation Theory

    • Gregg J. Zuckerman

    Pages 283-290

19. Back Matter

    Pages 291-296

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This volume is the result of a conference on Representation Theory of Reductive Groups held in Park City, Utah, April 16-20, 1982, under the auspices of the Department of Mathematics, University of Utah. Funding for the conference was provided by the National Science Foundation. The text includes a number of original papers together with expository articles on work already in print. It is hoped that the volume will be of use to both experts in the field and nonspecialists interested in obtaining some insight into the area. Principal organizers of the conference were Henryk Hecht, Dragan Mili~ie, and Peter Trombi. They would like to express their thanks to the National Science Foundation for their support, to the speakers for their diligence in submitting their manuscripts, and to Carla Curtis, Karen Edge, and Katherine Ruth, for typing the manuscripts which were contributed. v CONTENTS J. Arthur, Multipliers and a Paley-Wiener theorem for real reductive groups .......................................... .

• Group representation
• cohomology
• lie group
• representation theory

• Department of Mathematics, University of Utah, Salt Lake City, USA

  P. C. Trombi

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