Geodesic
Factor-representation of the group $GL(\infty)$ and admissible representations $GL(\infty)^X$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003), pp. 524-556.

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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. 
@article{JMAG_2003_10_a6,
     author = {N. I. Nessonov},
     title = {Factor-representation of the group $GL(\infty)$ and admissible representations $GL(\infty)^X$},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {524--556},
     publisher = {mathdoc},
     volume = {10},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_a6/}
}
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N. I. Nessonov. Factor-representation of the group $GL(\infty)$ and admissible representations $GL(\infty)^X$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003), pp. 524-556. http://geodesic.mathdoc.fr/item/JMAG_2003_10_a6/