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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 61; 1997; 479 ppMSC: Primary 11; 17; 22; 43;
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
ReadershipGraduate students and research mathematicians interested in Lie groups, harmonic analysis or algebraic number theory.

Table of Contents

Articles

A. W. Knapp  Structure theory of semisimple Lie groups [ MR 1476489 ]

Peter Littelmann  Characters of representations and paths in $\mathfrak {H}^*_{\mathrm {R}}$ [ MR 1476490 ]

Robert W. Donley, Jr.  Irreducible representations of $\mathrm {SL}(2, \mathbf {R})$ [ MR 1476491 ]

M. Welleda Baldoni  General representation theory of real reductive Lie groups [ MR 1476492 ]

Patrick Delorme  Infinitesimal character and distribution character of representations of reductive Lie groups [ MR 1476493 ]

Wilfried Schmid and Vernon Bolton  Discrete series [ MR 1476494 ]

Robert W. Donley, Jr.  The BorelWeil theorem for $\mathrm {U}(n)$ [ MR 1476495 ]

E. P. van den Ban  Induced representations and the Langlands classification [ MR 1476496 ]

C. Moeglin  Representations of $\mathrm {GL}(n)$ over the real field [ MR 1476497 ]

Sigurdur Helgason  Orbital integrals, symmetric Fourier analysis, and eigenspace representations [ MR 1476498 ]

E. P. van den Ban, M. FlenstedJensen and H. Schlichtkrull  Harmonic analysis on semisimple symmetric spaces: a survey of some general results [ MR 1476499 ]

David A. Vogan, Jr.  Cohomology and group representations [ MR 1476500 ]

A. W. Knapp  Introduction to the Langlands program [ MR 1476501 ]

C. Moeglin  Representations of $\mathrm {GL}(n,F)$ in the nonArchimedean case [ MR 1476502 ]

Hervé Jacquet  Principal $L$functions for $\mathrm {GL}(n)$ [ MR 1476503 ]

Jonathan D. Rogawski  Functoriality and the Artin conjecture [ MR 1476504 ]

A. W. Knapp  Theoretical aspects of the trace formula for $\mathrm {GL}(2)$ [ MR 1476505 ]

Hervé Jacquet  Note on the analytic continuation of Eisenstein series: An appendix to “Theoretical aspects of the trace formula for $\mathrm {GL}(2)$” [in Representation theory and automorphic forms (Edinburgh, 1996), 355–405, Proc. Sympos. Pure Math., 61, Amer. Math. Soc., Providence, RI, 1997; MR1476505 (98k:11062)] by A. W. Knapp [ MR 1476506 ]

A. W. Knapp and J. D. Rogawski  Applications of the trace formula [ MR 1476507 ]

James Arthur  Stability and endoscopy: informal motivation [ MR 1476508 ]

Hervé Jacquet  Automorphic spectrum of symmetric spaces [ MR 1476509 ]

Robert P. Langlands  Where stands functoriality today? [ MR 1476510 ]


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

Articles

A. W. Knapp  Structure theory of semisimple Lie groups [ MR 1476489 ]

Peter Littelmann  Characters of representations and paths in $\mathfrak {H}^*_{\mathrm {R}}$ [ MR 1476490 ]

Robert W. Donley, Jr.  Irreducible representations of $\mathrm {SL}(2, \mathbf {R})$ [ MR 1476491 ]

M. Welleda Baldoni  General representation theory of real reductive Lie groups [ MR 1476492 ]

Patrick Delorme  Infinitesimal character and distribution character of representations of reductive Lie groups [ MR 1476493 ]

Wilfried Schmid and Vernon Bolton  Discrete series [ MR 1476494 ]

Robert W. Donley, Jr.  The BorelWeil theorem for $\mathrm {U}(n)$ [ MR 1476495 ]

E. P. van den Ban  Induced representations and the Langlands classification [ MR 1476496 ]

C. Moeglin  Representations of $\mathrm {GL}(n)$ over the real field [ MR 1476497 ]

Sigurdur Helgason  Orbital integrals, symmetric Fourier analysis, and eigenspace representations [ MR 1476498 ]

E. P. van den Ban, M. FlenstedJensen and H. Schlichtkrull  Harmonic analysis on semisimple symmetric spaces: a survey of some general results [ MR 1476499 ]

David A. Vogan, Jr.  Cohomology and group representations [ MR 1476500 ]

A. W. Knapp  Introduction to the Langlands program [ MR 1476501 ]

C. Moeglin  Representations of $\mathrm {GL}(n,F)$ in the nonArchimedean case [ MR 1476502 ]

Hervé Jacquet  Principal $L$functions for $\mathrm {GL}(n)$ [ MR 1476503 ]

Jonathan D. Rogawski  Functoriality and the Artin conjecture [ MR 1476504 ]

A. W. Knapp  Theoretical aspects of the trace formula for $\mathrm {GL}(2)$ [ MR 1476505 ]

Hervé Jacquet  Note on the analytic continuation of Eisenstein series: An appendix to “Theoretical aspects of the trace formula for $\mathrm {GL}(2)$” [in Representation theory and automorphic forms (Edinburgh, 1996), 355–405, Proc. Sympos. Pure Math., 61, Amer. Math. Soc., Providence, RI, 1997; MR1476505 (98k:11062)] by A. W. Knapp [ MR 1476506 ]

A. W. Knapp and J. D. Rogawski  Applications of the trace formula [ MR 1476507 ]

James Arthur  Stability and endoscopy: informal motivation [ MR 1476508 ]

Hervé Jacquet  Automorphic spectrum of symmetric spaces [ MR 1476509 ]

Robert P. Langlands  Where stands functoriality today? [ MR 1476510 ]