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

Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the q-Onsager algebra Oq. 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 Δq. There is a natural algebr...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Terwilliger, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209528
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The q-Onsager Algebra and the Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 34 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the q-Onsager algebra Oq. 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 Δq. There is a natural algebra homomorphism ♮: Oq → Δq. We apply ♮ 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.
ISSN:1815-0659