Harmonic Analysis on Reductive Groups

✍ Scribed by Jeffrey Adams (auth.), Prof. William H. Barker, Prof. Paul J. Sally Jr. (eds.)

• Publisher: Birkhäuser Basel
• Year: 1991
• Tongue: English
• Leaves: 394
• Series: Progress in Mathematics 101
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Lifting of Characters....Pages 1-50
Handling the Inverse Spherical Fourier Transform....Pages 51-56
Some Problems in Local Harmonic Analysis....Pages 57-78
Asymptotic Expansions on Symmetric Spaces....Pages 79-87
The Admissible Dual of GL N Via Restriction to Compact Opent Subgroups....Pages 89-99
Invariant Harmonic Analysis on the Schwartz Space of a Reductive p -ADIC Group....Pages 101-121
Constructing the Supercuspidal Representation of GL n ( F ), F p —ADIC....Pages 123-179
A Remark on the Dunkl Differential—Difference Operators....Pages 181-191
Invariant Differential Operators and Weyl Group Invariants....Pages 193-200
The Schwartz Space of a General Semisimple Lie Group....Pages 201-208
Intertwining Functors and Irreducibility of Standard Harish—Chandra Sheaves....Pages 209-222
Fundametal G —Strata....Pages 223-233
Construction and Classification of Irreducible Harish—Chandra Modules....Pages 235-275
Langlands’ Conjecture on Plancherel Measures for p -Adic Groups....Pages 277-295
Transfer and Descent: Some Recent Results....Pages 297-304
On Jacquet Modules of Induced Representations of p —Adic Symplectic Groups....Pages 305-314
Associated Varieties and Unipotent Representations....Pages 315-388
Back Matter....Pages 389-390

✦ Subjects

Abstract Harmonic Analysis; Group Theory and Generalizations