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.
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.
Lisainfo e-raamatute kohta