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Session III.7 - Special Functions and Orthogonal Polynomials

Wednesday, June 21, 14:30 ~ 15:00

Multivariate Racah polynomials and their algebras

Sarah Post

University of Hawaii   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, I will discuss recent results on the structure and representation theory of higher-rank extensions of the Racah algebra. The Racah algebra can be realized as a centralizer in the three-fold tensor coproduct of sl_2 and its representation theory is connected with univariate Racah polynomials. These bispectral polynomials satisfy a second-order difference equation as well as the usual three term recurrence. We will discuss how the structure is extended naturally in the algebra and the novel bivariate polynomials that arise. The structure of the algebra will be leveraged to discover alternate presentations of these polynomials through various paths in the commuation diagrams.

Joint work with Sebastien Bertrand.

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