Noncommutative Independence from Characters of the Infinite Symmetric\n Group mathbbs_\∞

2010/05/31 by Rolf Gohm, Gohm, Rolf, Claus Köstler +1
Mathematics · #20C32 #46L53 #60G09 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications #Representation Theory (math.RT) #math.OA #math.PR #math.RT #msc:20C32 #msc:46L53 #msc:60G09

paper · pdf · doi:10.48550/arxiv.1005.5726

47 pages

arxiv created 2010/05/31 · openalex publication_date 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an operator algebraic proof of a classical theorem of Thoma which\ncharacterizes the extremal characters of the infinite symmetric group\n mathbbS_\∞. Our methods are based on noncommutative conditional\nindependence emerging from exchangeability and we reinterpret Thoma's theorem\nas a noncommutative de Finetti type result. Our approach is, in parts, inspired\nby Jones' subfactor theory and by Okounkov's spectral proof of Thoma's theorem,\nand we link them by inferring spectral properties from certain commuting\nsquares.\n

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