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Titlebook: Asymptotic Combinatorics with Applications to Mathematical Physics; A European Mathemati Anatoly M. Vershik,Yuri Yakubovich Book 2003 Sprin

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An introduction to harmonic analysis on the infinite symmetric groupThe aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory—harmonic analysis for ..
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Characters of symmetric groups and free cumulantsWe investigate Kerov’s formula expressing the normalized irreducible characters of symmetric groups evaluated on a cycle, in terms of the free cumulants of the associated Young diagrams.
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Advances in Intelligent and Soft Computings, their representations, characters and other attributes as group rank grows to infinity. Another kind of questions (in the spirit of infinite dimensional analysis) deal with properties of infinite dimensional analogues of classical groups. Let us discuss, for instanse, the most simple nontrivial e
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Foundations of Intelligent Systemst of the evaluation modules over the algebras H .x and H..The module . depends on two partitions λ of . and . of ., and on two complex numbers.There is a canonical operator . acting in ., it corresponds to the Yang .-matrix.The algebra H. contains the symmetric group algebra ℂ S. as a subalgebra, an
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Asymptotic Combinatorics with Applications to Mathematical Physics978-3-540-44890-7Series ISSN 0075-8434 Series E-ISSN 1617-9692
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https://doi.org/10.1007/3-540-44890-XMeasure; Probability theory; Riemann-Hilbert problem; Young diagram; characters of the representations; m
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