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Representation Theory and Automorphic Forms
Edited by: T. N. Bailey, University of Edinburgh, Scotland, and A. W. Knapp, SUNY at Stony Brook
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Proceedings of Symposia in Pure Mathematics
1997; 479 pp; hardcover
Volume: 61
ISBN-10: 0-8218-0609-2
ISBN-13: 978-0-8218-0609-8
List Price: US$84
Member Price: US$67.20
Order Code: PSPUM/61
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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

  • 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 Borel-Weil 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. Flensted-Jensen, 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
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