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Representations of groups

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Representations of groups. --- Finite groups. --- Compact groups.

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Multiplicity diagrams can be viewed as schemes for describing the phenomenon of 'symmetry breaking' in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacanae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry. The book develops in detail some themes which were touched on in the highly successful Symplectic Techniques in Physics by V. Guillemin and S. Sternberg, including the geometry of the moment map, the Duistermaat-Heckman theorem, the interplay between coadjoint orbits and representation theory, and quantization. Students and researchers in geometry and mathematical physics will find this book fascinating.

Group theory. --- Quantum theory. --- Representations of groups. --- Symplectic groups.

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Group theory --- Hypergroups. --- Hypergroupes. --- Representations of groups. --- Représentations de groupes. --- Measure algebras. --- Algèbres de mesures. --- Hypergroups --- Measure algebras --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebras, Measure --- Harmonic analysis --- Measure theory

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Group theory --- p-adic fields. --- Groupes p-adiques. --- Symplectic groups. --- Groupes symplectiques. --- Representations of groups. --- Représentations de groupes. --- p-adic fields --- Representations of groups --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebraic fields --- p-adic numbers