2005/12/16 by A. M. Vershik, Vershik, A. M., Н. В. Цилевич +2
Mathematics · #05E05 #20C32 #60J80 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #math.PR #math.RT #msc:05E05 #msc:20C32 #msc:60J80
paper · pdf · doi:10.48550/arxiv.math/0512389
13 pages, Bibl 10
arxiv created 2005/12/16 · openalex publication_date 2005/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the class of inductive limits of the representations of finite symmetric groups with simple spectrum coinsides with the class of Markov representations of the infinite symmetric group associated with Markov measures on the space of infinite Young tableaux. We also show that the representations of infinite symmetric group induced from identity representation of two-block Young subgroup are Markov representations and find explicit formulas for transition probabilities of corresponding Markov measure on the Young diagrmas. Induced two-row representations of finite symmetric group are studied using tensor model of those representations which alows easily to obtain the formulas for Gel'fand-Zetlin basis.