Representation Theory of Lie Groups

M. F. Atiyah; R. Bott; S. Helgason; D. Kazhdan; B. Kostant; G. Lustztig

doi:10.1017/CBO9780511662683

Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten distinguished mathematicians designed to provide the reader with a deeper understanding of the fundamental theory and appreciate the range of results. This volume contains much to interest mathematicians and theoretical physicists from advanced undergraduate level upwards.

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Representation Theory of Lie Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

1 - Introduction
pp 1-2

PART I
pp 3-4

2 - Origins and early history of the theory of unitary group representations
pp 5-19

3 - Induced representations
pp 20-64

4 - The geometry and representation theory of compact Lie groups
pp 65-90

5 - Algebraic structure of Lie groups
pp 91-150

6 - Lie groups and physics
pp 151-175

7 - The Harish-Chandra character
pp 176-182

PART II
pp 183-184

8 - Representations of semi-simple Lie groups
pp 185-235

9 - Invariant differential operators and eigenspace representations
pp 236-286

10 - Quantization and representation theory
pp 287-316

11 - Integral geometry and representation theory
pp 317-324

12 - On the reflection representation of a finite Chevalley group
pp 325-338

Index
pp 339-341

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Representation Theory of Lie Groups

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