Induced Representations of Infinite Symmetric Group
| dc.creator | Tsilevich, N. V. | |
| dc.creator | Vershik, A. M. | |
| dc.date | 2006-05-06 | |
| dc.date.accessioned | 2026-07-07T07:13:58Z | |
| dc.date.available | 2026-07-07T07:13:58Z | |
| dc.description | 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. | |
| dc.description | 25 pp., Ref.23 | |
| dc.identifier | https://arxiv.org/abs/math/0605166 | |
| dc.identifier | http://arxiv.org/abs/math/0605166 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112683 | |
| dc.subject | Representation Theory | |
| dc.subject | Operator Algebras | |
| dc.subject | 20C32,43A65,43A40 | |
| dc.title | Induced Representations of Infinite Symmetric Group | |
| dc.type | text |