## Lectures on Lie Groups"[ Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky |

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Beautiful book. Reads like a novel. If you're a mathematician, anyway.

### Contents

BASIC DEFINITIONS | 3 |

ONEPARAMETER SUBGROUPS THE EXPONENTIAL MAP ETC | 9 |

ELEMENTARY REPRESENTATION THEORY | 24 |

MAXIMAL TORI IN LIE GROUPS | 81 |

GEOMETRY OF THE STIEFEL DIAGRAM | 103 |

REPRESENTATION THEORY | 144 |

REPRESENTATIONS OF THE CLASSICAL GROUPS | 167 |

182 | |

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### Common terms and phrases

Abelian algebra bilinear called Chapter character chart choose class function closed commutes compact complex component conjugate connected Consider consists construct contains continuous COROLLARY corresponding course covering define DEFINITION diagram differential dimension eigenspace element elementary equivalent EXAMPLE factors FDWC finite fixed point follows function function f G-map G-space given gives Hence Hermitian form homomorphism Horn V,W identity induced integer invariant under G irreducible representations isomorphism LEMMA Let G Lie group lies lifts linear lower terms manifold matrices maximal torus neighbourhood Note path permutes plane polynomial positive roots Proof PROPOSITION prove quaternionic reflection REMARK result ring runs self-conjugate Similarly simple roots smooth splits structure map SU(n subgroup Suppose symmetric THEOREM theory trivially vector space weights Weyl chamber write written zero