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arXiv · 1509.08719

Center of the universal Askey--Wilson algebra at roots of unity

Hau-Wen Huang
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Abstract

Inspired by a profound observation on the Racah--Wigner coefficients of $U_q(\mathfrak{sl}_2)$, the Askey--Wilson algebras were introduced in the early 1990s. A universal analog $\triangle_q$ of the Askey--Wilson algebras was recently studied. For $q$ not a root of unity, it is known that $Z(\triangle_q)$ is isomorphic to the polynomial ring of four variables. A presentation for $Z(\triangle_q)$ at $q$ a root of unity is displayed in this paper. As an application, a presentation for the center of the double affine Hecke algebra of type $(C_1^\vee,C_1)$ at roots of unity is obtained.

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BibTeXRIS

Hau-Wen Huang. 2017-11-29. Center of the universal Askey--Wilson algebra at roots of unity. https://doi.org/10.1016/j.nuclphysb.2016.05.006

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