Abstract
We 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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References
Biane, P.:Representations of symmetric groups and free probability.Adv. Math.,138, 126–181 (1998)
Ivanov, V., Olshanski, G.: Kerov’s central limit theorem for the Plancherel measure on Young diagrams.Preprint (June2001)
Kerov, S.V.: Transition probabilities of continual Young diagrams and the Markov moment problem.Funct.Anal.Appl.,27, 104–117 (1993)
Kerov, S.V.: Talk at IHP conference (January2000)
Kerov, S.V., Olshanski, G.: Polynomial functions on the set of Young diagrams.C.R.Acad.Sci.Paris Sér.I Math.,319, no.2, 121–126 (1994)
Lascoux, A., Schützenberger, M.P.: Treillis et bases des groupes de Coxeter. Electron.J.Combin.3, no.2, Research paper 27, 35 pp.(1996)
Macdonald, I.G.: Symmetric functions and Hall polynomials, Second Edition.Oxford Univ.Press, Oxford (1995)
Molev, A.I.: Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra.Proceedings of the 7th Conference on Formal Power Series and Algebraic Combinatorics (Noisy-le-Grand,1995).Discrete Math.,180, no.1–3, 281–300 (1998)
Okounkov, A.:Private communication (January2001)
Speicher, R.: Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory.Memoirs of the AMS,627 (1998)
Stanley, R.:Private communication (May2001)
Stanley, R.:Irreducible symmetric group characters of rectangular shape. Preprint (September 2001)
Speicher, R., Woroudi, R.:Boolean independence.In:Voiculescu, D.(ed)Free probability, Fields Institue Communications, 267–280 (1996)
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Biane, P. (2003). Characters of symmetric groups and free cumulants. 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_8
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DOI: https://doi.org/10.1007/3-540-44890-X_8
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