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On certain class of unitarizable representations of the Lie algebra \(u(p,q)\). (English) Zbl 0752.17004
Geometry and physics, Proc. Winter Sch., Srni/Czech. 1990, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 26, 207-215 (1991).
[For the entire collection see Zbl 0742.00067.]
T. J. Enright and V. S. Varadarajan [Ann. Math., II. Ser. 102, 1-15 (1975; Zbl 0304.22011)] defined a certain class of irreducible representations of a noncompact semisimple Lie group related to a Hermitian symmetric space which are called Enright-Varadarajan representations. The author finds a subclass of unitarizable Enright- Varadarajan representations of the Lie algebra \(u(p,q)\) of the group \(U(p,q)\). The orthonormal bases are constructed for them which are an analogue of the Gel’fand-Tsetlin basis. It is interesting that the Gel’fand-Graev representations of the Lie algebra \(u(p,q)\) belong to the subclass of unitary representations obtained in this article.
Reviewer: A.Klimyk (Kiev)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E46 Semisimple Lie groups and their representations