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Introduction to the Representation Theory of Compact and Locally Compact Groups : London Mathematical Society Lecture Note Series - Alain Robert

Introduction to the Representation Theory of Compact and Locally Compact Groups

London Mathematical Society Lecture Note Series

Paperback

Published: 11th April 1983
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Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Representations of compact groups
Compact groups and Haar measures
Representations, general constructions
A geometrical application
Finite-dimensional representations of compact groups
Decomposition of the regular representation
Convolution, Plancherel formula & Fourier inversion
Characters and group algebras
Induced representations and Frobenius-Weil reciprocity
Tannaka duality
Representations of the rotation group
Representations of Locally Compact Groups
Groups with few finite-dimensional representations
Invariant measures on locally compact groups and homogeneous spaces
Continuity properties of representations
Representations of G and of L1(G)
Schur's lemma: unbounded version
Discrete series of locally compact groups
The discrete series of S12(R)
The principal series of S12(R)
Decomposition along a commutative subgroup
Type I groups
Getting near an abstract Plancherel formula
Epilogue
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521289757
ISBN-10: 0521289750
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 216
Published: 11th April 1983
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.4
Weight (kg): 0.32