Proceedings of Symposia in Pure Mathematics 1997; 479 pp; hardcover Volume: 61 ISBN10: 0821806092 ISBN13: 9780821806098 List Price: US$89 Member Price: US$71.20 Order Code: PSPUM/61
 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 representationtheoretic 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  A. W. Knapp  Structure theory of semisimple Lie groups
 P. Littelmann  Characters of representations and paths in \({\mathfrak h}^*_{\mathbb R}\)
 R. W. Donley, Jr.  Irreducible representations of SL(2,R)
 M. W. Baldoni  General representation theory of real reductive Lie groups
 P. Delorme  Infinitesimal character and distribution character of representations of reductive Lie groups
 W. Schmid and V. Bolton  Discrete series
 R. W. Donley, Jr.  The BorelWeil theorem for \(U(n)\)
 E. P. van den Ban  Induced representations and the Langlands classification
 C. Mœglin  Representations of GL(n) over the real field
 S. Helgason  Orbital integrals, symmetric Fourier analysis, and eigenspace representations
 E. P. van den Ban, M. FlenstedJensen, and H. Schlichtkrull  Harmonic analysis on semisimple symmetric spaces: A survey of some general results
 D. A. Vogan, Jr.  Cohomology and group representations
 A. W. Knapp  Introduction to the Langlands program
 C. Mœglin  Representations of GL(n,F) in the nonarchimedean case
 H. Jacquet  Principal \(L\)functions for \(GL(n)\)
 J. D. Rogawski  Functoriality and the Artin conjecture
 A. W. Knapp  Theoretical aspects of the trace formula for \(GL(2)\)
 H. Jacquet  Note on the analytic continuation of Eisenstein series: An appendix to the previous paper
 A. W. Knapp and J. D. Rogawski  Applications of the trace formula
 J. Arthur  Stability and endoscopy: Informal motivation
 H. Jacquet  Automorphic spectrum of symmetric spaces
 R. P. Langlands  Where stands functoriality today?
 Index
