## Introduction to the Representation Theory of Compact and Locally Compact GroupsBecause 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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