NDLI: Macdonald operators at infinity

Content Provider	Springer Nature Link
Author	Nazarov, M. L. Sklyanin, E. K.
Copyright Year	2013
Abstract	We construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables x $_{1}$,x $_{2}$,… and of two parameters q,t are their eigenfunctions. These operators are defined as limits at N→∞ of renormalized Macdonald operators acting on symmetric polynomials in the variables x $_{1}$,…,x $_{ N }$. They are differential operators in terms of the power sum variables $p_{n}=x_{1}^{n}+x_{2}^{n}+\cdots$ and we compute their symbols by using the Macdonald reproducing kernel. We express these symbols in terms of the Hall–Littlewood symmetric functions of the variables x $_{1}$,x $_{2}$,…. Our result also yields elementary step operators for the Macdonald symmetric functions.
Starting Page	23
Ending Page	44
Page Count	22
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	40
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2013-09-27
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Macdonald symmetric functions Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Macdonald operators at infinity