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Unitary representations of infinite-dimensional pairs \((G,K)\) and the formalism of R. Howe. (English. Russian original) Zbl 0532.22019
Sov. Math., Dokl. 27, 290-294 (1983); translation from Dokl. Akad. Nauk SSSR 269, 33-36 (1983).
Let \(G\) and \(K\) be the inductive limits \(\cup_n \mathrm{U}(n)\) and \(\cup_n \mathrm{SO}(n)\) of the classical groups \(\mathrm{U}(n)\) and \(\mathrm{SO}(n)\). A unitary representation of \(G\) is called “admissible for the pair \((G,K)\)” if its restriction to \(K\) fulfills certain conditions. The author studies and constructs admissible representations for the pair \((G,K)\) and for several other pairs of inductive limits of classical or symmetric groups.

22D10 Unitary representations of locally compact groups
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties