Algebra of differential operators associated with Young diagrams
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.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- February 2012
- DOI:
- 10.1016/j.geomphys.2011.09.001
- arXiv:
- arXiv:1012.0433
- Bibcode:
- 2012JGP....62..148M
- Keywords:
-
- Mathematics - Geometric Topology;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Combinatorics
- E-Print:
- 11 pages