Open Access

A description of characters on the infinite wreath product


Abstract

Let $\mathfrak{S}_\infty$ be the infinity permutation group and $\Gamma$ an arbitrary group. Then $\mathfrak{S}_\infty$ admits a natural action on $\Gamma^\infty$ by automorphisms, so one can form a semidirect product $\Gamma^\infty \times \mathfrak{S}_\infty$, known as the wreath product $\Gamma\wr\mathfrak{S}_\infty$ of $\Gamma$ by $\mathfrak{S}_{\infty}$. We obtain a full description of unitary $I\!I_1-$factor-representations of $\Gamma\wr\mathfrak{S}_\infty$ in terms of finite characters of $\Gamma$. 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 $I\!I\!I$, where the modular operator of Tomita-Takesaki expresses naturally by the asymptotic operators, which are important in the theory of characters of $\mathfrak{S}_\infty$.


Full Text





Article Information

TitleA description of characters on the infinite wreath product
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 301-317
MathSciNet MR2374832
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

A. V. Dudko
Kharkiv National University, Kharkiv, Ukraine

N. I. Nessonov
Department of Mathematics, Institute For Low Temperature Physics and Engineering, 47 Lenin Avenue, Kharkiv, Ukraine 


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



Citation Example

A. V. Dudko and N. I. Nessonov, A description of characters on the infinite wreath product, Methods Funct. Anal. Topology 13 (2007), no. 4, 301-317.


BibTex

@article {MFAT391,
    AUTHOR = {Dudko, A. V. and Nessonov, N. I.},
     TITLE = {A description of characters on the infinite wreath product},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {301-317},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=391},
}


All Issues