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Elliptic Analogues of the Macdonald and Koornwinder Polynomials

Rains, Eric M. (2011) Elliptic Analogues of the Macdonald and Koornwinder Polynomials. In: Proceedings of the International Congress of Mathematicians 2010. Hindustan Book Agency , New Delhi, India, pp. 2530-2554. ISBN 978-81-85931-08-3. https://resolver.caltech.edu/CaltechAUTHORS:20170925-124323959

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Abstract

Perhaps the nicest multivariate orthogonal polynomials are the Macdonald and Koornwinder polynomials, respectively 2-parameter deformations of Schur functions and 6-parameter deformations of orthogonal and symplectic characters, satisfying a trio of nice properties known as the Macdonald “conjectures”. In recent work, the author has constructed elliptic analogues: a family of multivariate functions on an elliptic curve satisfying analogues of the Macdonald conjectures, and degenerating to Macdonald and Koornwinder polynomials under suitable limits. This article will discuss the two main constructions for these functions, focusing on the more algebraic/combinatorial of the two approaches.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/9789814324359_0157DOIArticle
http://www.worldscientific.com/doi/abs/10.1142/9789814324359_0157PublisherArticle
Additional Information:© 2011 Hindustan Book Agency. Partially supported by the NSF, grant no. DMS-0401387.
Funders:
Funding AgencyGrant Number
NSFDMS-0401387
Subject Keywords:Macdonald polynomials, elliptic curves, special functions
Classification Code:Mathematics Subject Classification (2010): Primary 33D52, Secondary 14H52
Record Number:CaltechAUTHORS:20170925-124323959
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170925-124323959
Official Citation:Elliptic Analogues of the Macdonald and Koornwinder Polynomials Eric M. Rains Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). June 2011, 2530-2554
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81813
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 20:26
Last Modified:03 Oct 2019 18:47

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