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This article is cited in 15 scientific papers (total in 15 papers)
The $q$-Onsager Algebra and the Universal Askey–Wilson Algebra
Paul Terwilliger Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA
Abstract:
Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the $q$-Onsager algebra $\mathcal O_q$. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we bring in the universal Askey–Wilson algebra $\Delta_q$. There is a natural algebra homomorphism $\natural \colon \mathcal O_q \to \Delta_q$. We apply $\natural $ to the above PBW basis, and express the images in closed form. Our results make heavy use of the Chebyshev polynomials of the second kind.
Keywords:
$q$-Onsager algebra; universal Askey–Wilson algebra; Chebyshev polynomial.
Received: January 25, 2018; in final form May 1, 2018; Published online May 7, 2018
Citation:
Paul Terwilliger, “The $q$-Onsager Algebra and the Universal Askey–Wilson Algebra”, SIGMA, 14 (2018), 044, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1343 https://www.mathnet.ru/eng/sigma/v14/p44
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Abstract page: | 154 | Full-text PDF : | 30 | References: | 17 |
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