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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subfactors arising from asymptotic representations of symmetric groups


Author: Makoto Yamashita
Journal: Proc. Amer. Math. Soc. 140 (2012), 249-261
MSC (2000): Primary 46L37; Secondary 20C32, 46L55
Published electronically: May 20, 2011
MathSciNet review: 2833537
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Abstract: We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial representation of the larger group. We compute subfactor invariants of this construction in terms of the Thoma parameter.


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Additional Information

Makoto Yamashita
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan
Email: makotoy@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10991-2
PII: S 0002-9939(2011)10991-2
Keywords: Subfactor, symmetric group, asymptotic representation
Received by editor(s): November 27, 2009
Received by editor(s) in revised form: June 15, 2010, July 13, 2010, and November 10, 2010
Published electronically: May 20, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.