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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2018
1. Verfasser: Terwilliger, P.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/209528
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Zitieren: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
id nasplib_isofts_kiev_ua-123456789-209528
record_format dspace
spelling Terwilliger, P.
2025-11-24T10:42:15Z
2018
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.
1815-0659
2010 Mathematics Subject Classification: 33D80; 17B40
arXiv: 1801.06083
https://nasplib.isofts.kiev.ua/handle/123456789/209528
https://doi.org/10.3842/SIGMA.2018.044
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.
The author thanks Pascal Baseilhac and Samuel Belliard for giving this paper a close reading and offering valuable suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The q-Onsager Algebra and the Universal Askey-Wilson Algebra
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The q-Onsager Algebra and the Universal Askey-Wilson Algebra
spellingShingle The q-Onsager Algebra and the Universal Askey-Wilson Algebra
Terwilliger, P.
title_short The q-Onsager Algebra and the Universal Askey-Wilson Algebra
title_full The q-Onsager Algebra and the Universal Askey-Wilson Algebra
title_fullStr The q-Onsager Algebra and the Universal Askey-Wilson Algebra
title_full_unstemmed The q-Onsager Algebra and the Universal Askey-Wilson Algebra
title_sort q-onsager algebra and the universal askey-wilson algebra
author Terwilliger, P.
author_facet Terwilliger, P.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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
url https://nasplib.isofts.kiev.ua/handle/123456789/209528
citation_txt 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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