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arXiv · 1801.06083

The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra

Paul Terwilliger
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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.

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BibTeXRIS

Paul Terwilliger. 2018-01-18. The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra. https://doi.org/10.3842/sigma.2018.044

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