Geodesic
Stable representations of the infinite symmetric group
Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1184-1214

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     title = {Stable representations of the infinite symmetric group},
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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/