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. |
Contents
A geometrical application | 3 |
PeterWeyl theorem | 20 |
Tannaka duality | 90 |
Groups with few finitedimensional representations | 111 |
12 | 117 |
17 | 164 |
18 | 172 |
Decomposition along a commutative subgroup | 179 |
Type I groups | 187 |
Getting near an abstract Plancherel formula | 194 |
Epilogue | 201 |
Other editions - View all
Introduction to the Representation Theory of Compact and Locally Compact Groups Alain Robert No preview available - 1983 |
Common terms and phrases
Banach space canonical character circle group coefficient commutative compact subgroup conjugate continuous functions convergence convolution Corollary countable decomposition defined definition denote dimension discrete series dm(x dual dx dy End H equivalent factor representation finite dimensional representation follows formula functions f G-morphism G₁ G₂ group G H₁ H₂ Haar measure hence hermitian Hilbert space Hilbert-Schmidt operator homomorphism integral invariant measure invariant subspace irreducible representation isomorphism isotypical component kernel L¹(G L² G L²(G left regular representation left translations Let G locally compact group matrices multiplication Neumann algebra non-zero orthonormal basis Plancherel polynomials Proof Proposition prove regular representation representation of G right regular representation right translates rotation scalar operator scalar product Schur's lemma SO₂ space H subset theorem topology unimodular unitary irreducible representation unitary representation V₁ V₂ vector space von Neumann algebra