Algebra of differential operators associated with Young diagrams

Details Algebra of differential operators associated with Young diagrams Algebra of differential operators associated with Young diagrams

2010-12-02

arxiv.org/abs/1012.0433v1

Journal of Geometry and Physics 62 (2012), pp. 148-155

Mathematics

Geometric Topology

11 pages

Scientific paper

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.

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