NDLI: Symmetric and nonsymmetric Koornwinder polynomials in the $$q \rightarrow 0$$ limit

Content Provider	Springer Nature Link
Author	Venkateswaran, Vidya
Copyright Year	2015
Abstract	Koornwinder polynomials are a 6-parameter $$BC_{n}$$ -symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case, standard constructions via difference operators do not allow one to directly control these polynomials at $$q=0$$ . In the first part of this paper, we provide an explicit construction for these polynomials in this limit, using the defining properties of Koornwinder polynomials. Our formula is a first step in developing the analogy between Hall–Littlewood polynomials and Koornwinder polynomials at $$q=0$$ . In the second part of the paper, we provide a construction for the nonsymmetric Koornwinder polynomials in the same limiting case; this parallels work by Descouens–Lascoux in type $$A$$ . As an application, we prove an integral identity for Koornwinder polynomials at $$q=0$$ .
Ending Page	364
Page Count	34
Starting Page	331
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	2
Volume Number	42
Language	English
Publisher	Springer US
Publisher Date	2015-02-07
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Symmetric functions Convex and Discrete Geometry Orthogonal polynomials Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) Computer Science Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Hecke algebras Combinatorics Koornwinder polynomials Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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