**Mathematical Surveys and Monographs**

Volume: 31;
1989;
350 pp;
Hardcover

MSC: Primary 22;

**Print ISBN: 978-0-8218-1526-7
Product Code: SURV/31**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-1258-6
Product Code: SURV/31.E**

List Price: $124.00

AMS Member Price: $99.20

MAA Member Price: $111.60

# Representation Theory and Harmonic Analysis on Semisimple Lie Groups

Share this page *Edited by *
*Paul J. Sally, Jr.; David A. Vogan, Jr.*

This book brings together five papers that have been influential in the study
of Lie groups. Though published more than 20 years ago, these papers made
fundamental contributions that deserve much broader exposure. In addition, the
subsequent literature that has subsumed these papers cannot replace the
originality and vitality they contain. The editors have provided a brief
introduction to each paper, as well as a synopsis of the major developments
which have occurred in the area covered by each paper.

Included here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's
thesis is closely related to Trombi's paper insofar as both deal with harmonic
analysis on real semisimple Lie groups, and, in particular, analysis on the
Schwartz space of Harish-Chandra. Arthur's thesis is concerned with the image
under the Fourier transform of the Schwartz space of a semisimple Lie group of
real rank one, while Trombi's paper provides an expository account of the
harmonic analysis associated to the decomposition of the Schwartz space under
the regular representation. In his thesis, Osborne extends the Atiyah-Bott
fixed point theorem for elliptic complexes to obtain a fixed point formula for
complexes that are not elliptic. Schmid proves a generalization of the
Borel-Weil theorem concerning an explicit and geometric realization of the
irreducible representations of a compact, connected semisimple Lie group.
Langlands's fundamental paper provides a classification of irreducible,
admissible representations of real reductive Lie groups.

#### Table of Contents

# Table of Contents

## Representation Theory and Harmonic Analysis on Semisimple Lie Groups

- Contents vii8 free
- Preface ix10 free
- List of Contributors xi12 free
- Introduction 114 free
- Harmonic analysis of tempered distributions on semisimple Lie groups ofreal rank one 1326 free
- On the classification of irreducible representations of real algebraic groups 101114
- Lefschetz formulas on nonelliptic complexes 171184
- Homogeneous complex manifolds and representations of semisimple Liegroups 223236
- On Harish-Chandra's theory of the Eisenstein integral for real semisimple Lie groups 287300