Stable representations of the infinite symmetric group
Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1184-1214
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We study the notion of a stable unitary representation of a group
(or a $\star$-representation of a $\mathbf C^\star$-algebra) with respect to some
group of automorphisms of the group (or algebra). In the case of the group of
finitary permutations of a countable set we give a complete description,
up to quasi-equivalence, of the representations which are
stable with respect to the group of all automorphisms of the group.
In particular, we solve an old question
concerning factor representations associated with Ol'shansky–Okun'kov
admissible representations. It is proved that these representations are induced
by factor representations of type ${\rm II}_1$ of two-block Young subgroups.
The class of stable representations will be the subject of further research.
Keywords:
infinite symmetric group, stable representations, factor representations, characters, semidirect product
Mots-clés : groupoid model.
Mots-clés : groupoid model.
@article{IM2_2015_79_6_a3,
author = {A. M. Vershik and N. I. Nessonov},
title = {Stable representations of the infinite symmetric group},
journal = {Izvestiya. Mathematics },
pages = {1184--1214},
publisher = {mathdoc},
volume = {79},
number = {6},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a3/}
}
A. M. Vershik; N. I. Nessonov. Stable representations of the infinite symmetric group. Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1184-1214. http://geodesic.mathdoc.fr/item/IM2_2015_79_6_a3/