Abstract
This paper presents the working notes by S. V. Kerov (1946–2000) written in 1993. The author introduces a multidimensional analog of the classical hypergeometric distribution. This is a probability measure Mn on the set of Young diagrams contained in the rectangle with n rows and m columns. The fact that the expression for Mn defines a probability measure is a nontrivial combinatorial identity, which is proved in various ways. Another combinatorial identity analyzed in the paper expresses a certain coherence between the measures Mn and Mn+1. A connection with Selberg-type integrals is also pointed out. The work is motivated by harmonic analysis on the infinite-dimensional unitary group. Bibliography: 25 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 35–91.
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Kerov, S.V. Multidimensional Hypergeometric Distribution and Characters of the Unitary Group. J Math Sci 129, 3697–3729 (2005). https://doi.org/10.1007/s10958-005-0309-6
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DOI: https://doi.org/10.1007/s10958-005-0309-6