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

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• 作者：Hau-Wen Huang¹ ; ^{hauwenh@math.ncu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：909
• 期：Complete
• 页码：260-296
• 全文大小：500 K

文摘

Inspired by a profound observation on the Racah–Wigner coefficients of U_q(sl₂)$U_q({\mathfrak{sl}}_2)$, the Askey–Wilson algebras were introduced in the early 1990s. A universal analog △_q${△}_q$ of the Askey–Wilson algebras was recently studied. For q   not a root of unity, it is known that Z(△_q)$Z({△}_q)$ is isomorphic to the polynomial ring of four variables. A presentation for Z(△_q)$Z({△}_q)$ 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.