**Proceedings of Symposia in Pure Mathematics**

Volume: 61;
1997;
479 pp;
Hardcover

MSC: Primary 11; 17; 22; 43;

**Print ISBN: 978-0-8218-0609-8
Product Code: PSPUM/61**

List Price: $95.00

AMS Member Price: $76.00

MAA Member Price: $85.50

**Electronic ISBN: 978-0-8218-9364-7
Product Code: PSPUM/61.E**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

# Representation Theory and Automorphic Forms

Share this page *Edited by *
*T. N. Bailey; A. W. Knapp*

This book is a course in representation theory of semisimple groups,
automorphic forms and the relations between these two subjects written by some
of the world's leading experts in these fields. It is based on the 1996
instructional conference of the International Centre for Mathematical Sciences
in Edinburgh. The book begins with an introductory treatment of structure
theory and ends with an essay by Robert Langlands on the current status of
functoriality. All papers are intended to provide overviews of the topics they
address, and the authors have supplied extensive bibliographies to guide the
reader who wants more detail.

The aim of the articles is to treat representation theory with two goals in
mind: 1) to help analysts make systematic use of Lie groups in work on harmonic
analysis, differential equations, and mathematical physics and 2) to provide
number theorists with the representation-theoretic input to Wiles's proof of
Fermat's Last Theorem.

Features:

- Discussion of representation theory from many experts' viewpoints
- Treatment of the subject from the foundations through recent advances
- Discussion of the analogies between analysis of cusp forms and analysis on semisimple symmetric spaces, which have been at the heart of research breakthroughs for 40 years
- Extensive bibliographies

#### Readership

Graduate students and research mathematicians interested in Lie groups, harmonic analysis or algebraic number theory.

# Table of Contents

## Representation Theory and Automorphic Forms

- Contents v6 free
- Foreword vii8 free
- Structure Theory of Semisimple Lie Groups 110 free
- Characters of Representations and Paths in h[sup(*)][sub(R)] 2938
- Irreducible Representations of SL(2,R) 5160
- General Representation Theory of Real Reductive Lie Groups 6170
- Infinitesimal Character and Distribution Character of Representations of Reductive Lie Groups 7382
- Discrete Series 8392
- The Borel-Weil Theorem for U(n) 115124
- Induced Representations and the Langlands Classification 123132
- Representations of GL(n) over the Real Field 157166
- Orbital Integrals, Symmetric Fourier Analysis, and Eigenspace Representations 167176
- Harmonic Analysis on Semisimple Symmetric Spaces: A Survey of Some General Results 191200
- Cohomology and Group Representations 219228
- Introduction to the Langlands Program 245254
- Representations of GL(n,F) in the Nonarchimedean Case 303312
- Principal L-functions for GL(n) 321330
- Functoriality and the Artin Conjecture 331340
- Theoretical Aspects of the Trace Formula for GL(2) 355364
- Note on the Analytic Continuation of Eisenstein Series: An Appendix to the Previous Paper 407416
- Applications of the Trace Formula 413422
- Stability and Endoscopy: Informal Motivation 433442
- Automorphic Spectrum of Symmetric Spaces 443452
- Where Stands Functoriality Today? 457466
- Index 473482