Introduction to the Representation Theory of Compact and Locally Compact Groups

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Cambridge University Press, Feb 10, 1983 - Mathematics - 205 pages
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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.
  

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Contents

Compact groups and Haar measures p
3
Representations general constructions
13
A geometrical application
21
Finitedimensional representations of compact groups
29
Decomposition of the regular representation
40
Convolution Plancherel formula Fourier inversion
53
Characters and group algebras
63
Induced representations and FrobeniusWeil reciprocity
78
l2 Invariant measures on locally compact groups
117
l3 Continuity properties of representations
128
l4 Representations of G and of LG
144
l6 Discrete series of locally compact groups
151
l7 The discrete series of Sl2K
164
l8 The principal series of Sl2R
172
l9 Decomposition along a commutative subgroup
179
Type I groups
187

Tannaka duality
90
Groups with few finitedimensional representations lll
111
2l Getting near an abstract Plancherel formula
194
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<a href="http://www.cambridge.org">© Cambridge University Press</a ...
Cambridge University Press. 978-0-521-28975-7 - Introduction to the Representation Theory of Compact and Locally. Compact Groups. Alain Robert. Excerpt ...
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and Brown carefully discusses what is known at this time. The ...
64. BOOK REVIEWS. and Brown carefully discusses what is known at this time. The final chapter is. devoted to the construction of complete resolutions for ...
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STAT 260 Fall 2007 Homepage
Introduction to the representation theory of compact and locally compact groups. Author: Robert, Alain. Published: Cambridge University Press, 1983 ...
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