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International conference "Geometrical Methods in Mathematical Physics"
December 12, 2011 16:00, Moscow, Lomonosov Moscow State University
 


Full algebra of cut-and-join operators.

S. M. Natanzon

National Research University "Higher School of Economics"
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MP4 295.2 Mb

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S. M. Natanzon


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Abstract: We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations of the set of natural numbers. The Schur functions form a complete system of common eigenfunctions of these differential operators, and their eigenvalues are expressed through the characters of symmetric groups. The structure constants of the algebra are expressed through the Hurwitz numbers. The talk is based on a joint work with A. Mironov and A. Morozov.

Language: English

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