Compact Lie groups and their representations

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