Abstract
We give a noncommutative extension of Kerov’s central limit theorem for irreducible characters of the symmetric group with respect to the Plancherel measure [S.Kerov:C.R.Acad.Sci.Paris 316 (1993)]in the framework of algebraic probability theory.For adjacency operators associated with the cycle classes, we consider their decomposition according to the length function on the Cayley graph of the symmetric group.We develop a certain noncommutative central limit theorem for them, in which the limit picture is described by creation and annihilation operators on an analogue of the Fock space equipped with an orthonormal basis labelled by Young diagrams.The limit Gaussian measure in Kerov’s theorem appears as the spectral distribution of the field operators in our setting.
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Hora, A. (2003). A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group. In: Vershik, A.M., Yakubovich, Y. (eds) Asymptotic Combinatorics with Applications to Mathematical Physics. Lecture Notes in Mathematics(), vol 1815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44890-X_4
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DOI: https://doi.org/10.1007/3-540-44890-X_4
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