## Lectures on Lie groups and representations of locally compact groups |

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### Contents

Topological groups | 2 |

Local study of Lie groups | 6 |

Relations between Lie groups | 16 |

10 other sections not shown

### Common terms and phrases

adjoint analytic representation Annals of Math canonical map closed subgroup commutes compact neighbourhood compact set compact subset compact support compact topology complete consequence continuous function continuous linear form continuous operator field continuous representation continuous sum continuous vector field convergence convex compact convolution product coordinates countable decomposed operator decomposition define Definition denote dense differential operator element equivalent exists a neighbourhood fact factorial representation finite function f function on G GL(n Haar measure Hence Hilbert space invariant subspace irreducible representations isomorphism Lemma Let G Lie algebra Lie group G Lie subgroup linear map locally compact group locally compact space manifold map f map h matrix measure on G modulo normal subgroup obviously Plancherel formula positive measure proof Proposition prove real numbers regular representation representation of G satisfies subalgebra Theorem Theory topological group trivial unique unitary representation vector field vector space weakly closed