Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators. (14th October 2020)

• Record Type: Journal Article
• Authors: Gaboriaud, Julien; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei
• Is Part Of: Journal of physics. Volume 53:Number 44(2020)
• Publication Date: 2020-10-14
• Subjects: Sklyanin algebras -- Heun operators -- Askey–Wilson operators and polynomials -- q-para Racah polynomials; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abb340
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The q -difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras s k a 3 and s k a 4 . It is shown that the q -para Racah polynomials corresponding to a non-conventional truncation of the Askey–Wilson polynomials form a basis for a finite-dimensional representation of s k a 4 . The first order Heun operators defined by a degree raising condition on polynomials are shown to form a five-dimensional vector space that encompasses s k a 4 . The most general quadratic expression in the five basis operators and such that it raises degrees by no more than one is identified with the Heun–Askey–Wilson operator.