Geodesic
Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 82-84.

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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
Mots-clés : Ismagilov's conjecture. 
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A. V. Kosyak. Quasi-Invariant Measures and Irreducible Representations of the Inductive Limit of Special Linear Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 82-84. http://geodesic.mathdoc.fr/item/FAA_2004_38_1_a7/

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