Introduction to the Representation Theory of Compact and Locally Compact Groups

by Alain Robert

• ISBN13: 9780521289757
• ISBN10: 0521289750
• Format: Paperback
• Copyright: 1983-02-28
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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

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