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

N. I. Nessonov

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003), pp. 524-556.

Résumé

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