A description of characters on the infinite wreath product

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dc.creatorDudko, A. V.
dc.creatorNessonov, N. I.
dc.date2005-10-27
dc.date.accessioned2026-07-07T06:48:00Z
dc.date.available2026-07-07T06:48:00Z
dc.descriptionLet $\mathfrak{S}_\infty$ be the infinity permutation group and $Γ$ an arbitrary group. Then $\mathfrak{S}_\infty$ admits a natural action on $Γ^\infty$ by automorphisms, so one can form a semidirect product $Γ^\infty\rtimes \mathfrak{S}_\infty$, known as the {\it wreath} product $Γ\wr\mathfrak{S}_\infty$ of $Γ$ by $\mathfrak{S}_{\infty}$. We obtain a full description of unitary $II_1-$factor-representations of $Γ\wr\mathfrak{S}_\infty$ in terms of finite characters of $Γ$. Our approach is based on extending Okounkov's classification method for admissible representations of $\mathfrak{S}_\infty\times\mathfrak{S}_\infty$. Also, we discuss certain examples of representations of type $II_1$, where the {\it modular operator} of Tomita-Takesaki expresses naturally by the asymptotic operators, which are important in the characters-theory of infinite symmetric group.
dc.description33 pages. We receive the full description of the finite characters on the infinite wreath product
dc.identifierhttps://arxiv.org/abs/math/0510597
dc.identifierhttp://arxiv.org/abs/math/0510597
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103839
dc.subjectRepresentation Theory
dc.subject20C15, 20C32
dc.titleA description of characters on the infinite wreath product
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