This article is cited in 6 papers

Brief communications

Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups

A. V. Kosyak

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Unitary representations of the group $G=\operatorname{SL}_0(2\infty,\mathbb{R})=\varinjlim_{n}\operatorname{SL}(2n-1,\mathbb{R})$ are constructed. The construction uses $G$-quasi-invariant measures on some $G$-spaces that are subspaces of the space $\operatorname{Mat}(2\infty,\mathbb{R})$ of two-way infinite real matrices. We give a criterion for the irreducibility of these representations.

Keywords: infinite-dimensional special linear group, irreducible unitary representation, quasi-invariant measure, Ismagilov's conjecture.

UDC: 512.544.6

Received: 18.12.2002

DOI: 10.4213/faa99

 English version: Functional Analysis and Its Applications, 2004, 38:1, 67–68

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