Compact Lie groups and their representations

Part I. Introduction: Topological groups. Lie groups Linear groups Fundamental problems of representation theory Part II. Elementary theory: Compact Lie groups. Global theorem The infinitesimal method in representation theory Analytic continuation Irreducible representations of the group $\mathrm {U}(n)$ Tensors and Young diagrams Casimir operators Indicator systems and the Gelfand-Cetlin basis Characters Tensor product of two irreducible representations of $\mathrm {U}(n)$ Part III. General theory: Basic types of Lie algebras and Lie groups Classification of compact and reductive Lie algebras Compact Lie groups in the large Description of irreducible finite-dimensonal representations Infinitesimal theory (characters, weights, Casimir operators) Some problems of spectral analysis for finite-dimensional representations Appendix I. On infinite-dimensional representations of semisimple complex Lie groups Appendix II. Elements of the general theory of unitary representations of locally compact groups Appexdix III. Unitary symmetry in the class of elementary particles References Subject index.

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