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arXiv · 1107.3544

The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$

Paul Terwilliger
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Abstract

Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $\Delta$ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between $\Delta$ and the quantum algebra $U_q(\mathfrak{sl}_2)$. Our main result is an algebra injection from $\Delta$ into a relative of $U_q(\mathfrak{sl}_2)$; the relative is obtained from $U_q(\mathfrak{sl}_2)$ by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of $U_q(\mathfrak{sl}_2)$

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Paul Terwilliger. 2011-07-18. The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$. https://doi.org/10.3842/sigma.2011.099

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