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Last 60 years of unitary representation theory. (Japanese) Zbl 0609.22006

The theory of unitary representations began, as the author says, with the work of H. Weyl [Math. Z. 23, 271-309 (1925); ibid. 24, 328-376, 377-395 (1925)] on the finite-dimensional unitary represenations of compact Lie groups. The author gives a very readable survey on the history of the theory of unitary representations, centering around the topics of Plancherel formula of semi-simple Lie groups - especially, the monumental works of Harish-Chandra on the representation of semi-simple Lie groups.
The titles of the sections of this article are as follows: § 1 Representation theory of compact Lie groups, § 2 From finite dimensional representations to infinite dimensional representations, § 3 Representations of Lorentz groups, § 4 Relations with the theory of operator rings, § 5 Characters, § 6 Representations of complex semi-simple groups, § 7 Spherical functions, § 8 Discrete series of representations, § 9 Plancherel formula, § 10 Conclusions.
Reviewer: A.Morimoto

MSC:

22E46 Semisimple Lie groups and their representations
43A90 Harmonic analysis and spherical functions
22D10 Unitary representations of locally compact groups
22-02 Research exposition (monographs, survey articles) pertaining to topological groups
22-03 History of topological groups
01A60 History of mathematics in the 20th century
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