Induced Representations of Infinite Symmetric Group

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We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type~I or of type~II. Each Young subgroup corresponds to a partition of the set of positive integers; depending on the sizes of blocks of this partition, we divide Young subgroups into two classes: large and small subgroups. The first class gives representations of type I, in particular, irreducible representations. The most part of Young subgroups of the second class give representations of type~II and, in particular, von Neumann factors of type II. We present a number of various examples. The main problem is to find the so-called {it spectral measure of the induced representation.} The complete solution of this problem is given for two-block Young subgroups and subgroups with infinitely many singletons and finitely many finite blocks of length greater than one.
25 pp., Ref.23

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Representation Theory, Operator Algebras, 20C32,43A65,43A40

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http://salesiana.dossiersoluciones.com/handle/123456789/112683

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605166
 http://arxiv.org/abs/math/0605166

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arXiv