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

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### Contents

Topological groups | 2 |

Local study of Lie groups | 7 |

Relations between Lie groups | 16 |

9 other sections not shown

### Common terms and phrases

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