Harmonic Analysis on Reductive Groups

1. Front Matter

   Pages i-xii

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2. Lifting of Characters

   • Jeffrey Adams

   Pages 1-50

3. Handling the Inverse Spherical Fourier Transform

   • Jean-Philippe Anker

   Pages 51-56

4. Some Problems in Local Harmonic Analysis

   • James Arthur

   Pages 57-78

5. Asymptotic Expansions on Symmetric Spaces

   • Erik van den Ban, Henrik Schlichtkrull

   Pages 79-87

6. The Admissible Dual of GL _N Via Restriction to Compact Opent Subgroups

   • Colin J. Bushnell, Philip C. Kutzko

   Pages 89-99

7. Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-ADIC Group

   • Laurent Clozel

   Pages 101-121

8. Constructing the Supercuspidal Representation of GL _n (F), F p—ADIC

   • Lawrence Corwin

   Pages 123-179

9. A Remark on the Dunkl Differential—Difference Operators

   • Gerrit J. Heckman

   Pages 181-191

10. Invariant Differential Operators and Weyl Group Invariants

    • Sigurdur Helgason

    Pages 193-200

11. The Schwartz Space of a General Semisimple Lie Group

    • Rebecca A. Herb

    Pages 201-208

12. Intertwining Functors and Irreducibility of Standard Harish—Chandra Sheaves

    • Dragan Miličić

    Pages 209-222

13. Fundametal G—Strata

    • Lawrence Morris

    Pages 223-233

14. Construction and Classification of Irreducible Harish—Chandra Modules

    • Wilfried Schmid

    Pages 235-275

15. Langlands’ Conjecture on Plancherel Measures for p-Adic Groups

    • Freydoon Shahidi

    Pages 277-295

16. Transfer and Descent: Some Recent Results

    • Diana Shelstad

    Pages 297-304

17. On Jacquet Modules of Induced Representations of p—Adic Symplectic Groups

    • Marko Tadić

    Pages 305-314

18. Associated Varieties and Unipotent Representations

    • David A. Vogan Jr.

    Pages 315-388

19. Back Matter

    Pages 389-390

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A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Sym­ posium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in 1972, to cover local harmonic analysis on reductive groups in such detail and to such an extent. While the Williamstown conference was longer (three weeks) and somewhat broader (nilpotent groups, solvable groups, as well as semisimple and reductive groups), the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade. These lectures began at an introductory level and advanced to the current state of research. Sec­ ond, there was a series of single lectures in which the speakers presented an overview of their latest research.

• Fourier transform
• Irreducibility
• calculus
• harmonic analysis
• lie group

• Department of Mathematics, Bowdoin College, Brunswick, USA

  William H. Barker

• Department of Mathematics, University of Chicago, Chicago, USA

  Paul J. Sally

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