Representation Theory and Automorphic Forms: (Proceedings of Symposia in Pure Mathematics)

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: to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics and to provide number theorists with the representation-theoretic input to Wiles' proof of Fermat's Last Theorem. This book 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; and, extensive bibliographies.

Table of Contents:
Structure theory of semisimple Lie groups by A. W. Knapp Characters of representations and paths in ${\mathfrak h}^*_{\mathbb R}$ by P. Littelmann Irreducible representations of SL(2,R) by R. W. Donley, Jr. General representation theory of real reductive Lie groups by M. W. Baldoni Infinitesimal character and distribution character of representations of reductive Lie groups by P. Delorme Discrete series by W. Schmid and V. Bolton The Borel-Weil theorem for $U(n)$ by R. W. Donley, Jr. Induced representations and the Langlands classification by E. P. van den Ban Representations of GL(n) over the real field by C. Moeglin Orbital integrals, symmetric Fourier analysis, and eigenspace representations by S. Helgason Harmonic analysis on semisimple symmetric spaces: A survey of some general results by E. P. van den Ban, M. Flensted-Jensen, and H. Schlichtkrull Cohomology and group representations by D. A. Vogan, Jr. Introduction to the Langlands program by A. W. Knapp Representations of GL(n,F) in the nonarchimedean case by C. Moeglin Principal $L$-functions for $GL(n)$ by H. Jacquet Functoriality and the Artin conjecture by J. D. Rogawski Theoretical aspects of the trace formula for $GL(2)$ by A. W. Knapp Note on the analytic continuation of Eisenstein series: An appendix to the previous paper by H. Jacquet Applications of the trace formula by A. W. Knapp and J. D. Rogawski Stability and endoscopy: Informal motivation by J. Arthur Automorphic spectrum of symmetric spaces by H. Jacquet Where stands functoriality today? by R. P. Langlands Index.