Unitary representations of infinite-dimensional pairs \((G,K)\) and the formalism of R. Howe. (English. Russian original) Zbl 0532.22019

Ol’shanskiĭ, G. I.

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.

Reviewer: Franz Pauer (Innsbruck)

MSC:

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

Keywords:

inductive limits; irreducible representations; factor representations with trace; unitary tame representations; admissible unitary representation