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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 1, Pages 47–63
DOI: https://doi.org/10.4213/tvp145
(Mi tvp145)
 

This article is cited in 7 scientific papers (total in 8 papers)

Markov measures on Young tableaux and induced representations of an infinite symmetric group

A. M. Vershik, N. V. Tsilevich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
References:
Abstract: We show that the class of so-called Markov representations of the infinite symmetric group $\mathfrak{S}_{N}$, associated with Markov measures on the space of infinite Young tableaux, coincides with the class of simple representations, i.e., inductive limits of representations with simple spectrum. The spectral measure of an arbitrary representation of $\mathfrak{S}_{N}$ with simple spectrum is equivalent to a multi-Markov measure on the space of Young tableaux. We also show that the representations of $\mathfrak{S}_{N}$ induced from the identity representations of two-block Young subgroups are Markov and find explicit formulas for the transition probabilities of the corresponding Markov measures. The induced representations are studied with the help of the tensor model of two-row representations of the symmetric groups; in particular, we deduce explicit formulas for the Gelfand–Tsetlin basis in the tensor models.
Keywords: Markov measures, Young tableaux, induced representations, simple spectrum.
Received: 23.11.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 1, Pages 211–223
DOI: https://doi.org/10.1137/S0040585X97982189
Bibliographic databases:
Language: Russian
Citation: A. M. Vershik, N. V. Tsilevich, “Markov measures on Young tableaux and induced representations of an infinite symmetric group”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 47–63; Theory Probab. Appl., 51:1 (2007), 211–223
Citation in format AMSBIB
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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