Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe

G.I. Ol'shanskii (Olshanski) Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe In the collection Representation of Lie groups and related topics. PP. 269–463. Translated from the Russian. Edited by A. M. Vershik and D. P. Zhelobenko Adv. Stud. Contemp. Math., 7 Gordon and Breach Science Publishers, New York, 1990. xiv+557 pp. ISBN:2-88124-678-8 Abstract. In this article we study the unitary representations of infinite dimensional classical groups. The following problems are examined: the construction of unitary representations, proof of their irreducibility, pairwise non-equivalence, decomposition of tensor products, continuity of the representations in appropriate group topology, calculation of spherical functions, approximation of irreducible unitary representations T of a given infinite-dimensional group G by irreducible unitary representation T of the corresponding finite-dimensional classical groups G(n).