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

Abstract

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 △q of the Askey–Wilson algebras was recently studied. For q not a root of unity, it is known that Z(△q) is isomorphic to the polynomial ring of four variables. A presentation for 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 (C1∨,C1) at roots of unity is obtained.