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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2003 Volume 301, Pages 35–91 (Mi znsl939)

This article is cited in 2 papers

Multidimensional hypergeometric distribution, and characters of the unitary group

S. V. Kerov


Abstract: The present paper is the publication of work 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 $M_n$ on the set of Young diagrams contained in the rectangle with $n$ rows and $m$ columns. The fact that the expression for $M_n$ 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 compatibility of the measures $M_n$ and $M_{n+1}$. A link with Selberg type integrals is also pointed out. The work is motivated by the problem of harmonic analysis on the infinite-dimensional unitary group.

UDC: 519.217+517.986+519.117

Received: 15.09.2003


 English version:
Journal of Mathematical Sciences (New York), 2005, 129:2, 3697–3729

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