This article is cited in 5 papers

Factor-representation of the group $GL(\infty)$ and admissible representations $GL(\infty)^X$

N. I. Nessonov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: This article is the second part of the work in which classification of factor-representations of group $GL(\infty)$ is given. The criterium of unitary equivalence of spherical representations of the group $(GL(\infty)^X)$ functions on finite set $X$ with values in $GL(\infty)$ in terms of their parameters is received here. A conformity between factor-representations of group $GL(\infty)$ and spherical representations of group $(GL(\infty)^X)$ is constructed. The design of continuation on the group of motions which corresponds to group $(GL(\infty)^X)$ is given for the received spherical representations.

MSC: 46L55, 46L65

Received: 02.08.2002

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