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- W4246897891 abstract "Publisher SummaryThis chapter provides a fairly self-contained treatment of the abstract representation theory and reviews the relation of the theory to Harish-Chandra's Plancherel theorem. By the abstract representation theory it means the representation theory of C* algebras and locally compact groups. This subject is vast and the chapter discusses the development of only those parts of the theory that have a bearing on locally compact, separable groups and more specifically to real reductive groups. Thus, for the deeper theorems on C* algebras, it imposes the simplifying assumption that the algebra is separable. Also, rather than treating the general “tame” case (i.e., Type I), the chapter discusses CCR algebras (liminaire in the sense of Dixmier). The chapter has opted to give a self-contained treatment for two reasons. The first is that the new generation of researchers on the representation theory of reductive groups is largely ignorant of the general theory. The second reason is that it is felt that the theory of C* algebras could play an important role, even in the case of reductive groups." @default.
- W4246897891 created "2022-05-12" @default.
- W4246897891 date "1988-01-01" @default.
- W4246897891 modified "2023-10-16" @default.
- W4246897891 title "14 Abstract Representation Theory" @default.
- W4246897891 doi "https://doi.org/10.1016/s0079-8169(08)62839-1" @default.
- W4246897891 hasPublicationYear "1988" @default.
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