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

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Inspired by a profound observation on the Racah-Wigner coefficients of Uq(sl2), the Askey-Wilson algebras were introduced in the early 1990s. A universal analog Δq of the Askey-Wilson algebras was recently studied. For q not a root of unity, it is known that Z(Δq) is isomorphic to the polynomial ring of four variables. A presentation for Z(Δq) 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 (C1,C1) at roots of unity is obtained.

Original languageEnglish
Pages (from-to)260-296
Number of pages37
JournalNuclear Physics B
StatePublished - 1 Aug 2016


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