Algebra of differential operators associated with Young diagrams

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 co...

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Vydáno v:arXiv.org
Hlavní autoři: Mironov, A, Morozov, A, Natanzon, S
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 02.12.2010
Témata:
Algebra
Differential equations
Eigenvalues
Eigenvectors
Mathematical analysis
Number theory
Operators (mathematics)
Permutations
ISSN:2331-8422
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Shrnutí: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.
Bibliografie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1012.0433