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Let $\C$ denote the field of complex numbers, and fix a nonzero $q \in \C$such that $q^4 \ne 1$. Define a $\C$-algebra $\Delta_q$ by generators andrelations in the following way. The generators are $A,B,C$. The relationsassert that each of $A+\frac{qBC-q^{-1}CB}{q^2-q^{-2}}$,$B+\frac{qCA-q^{-1}AC}{q^2-q^{-2}}$, $C+\frac{qAB-q^{-1}BA}{q^2-q^{-2}}$ iscentral in $\Delta_q$. The algebra $\Delta_q$ is called the universalAskey-Wilson algebra. Let $\Gamma$ denote a distance-regular graph that has$q$-Racah type. Fix a vertex $x$ of $\Gamma$ and let $T=T(x)$ denote thecorresponding subconstituent algebra. In this paper we discuss a relationshipbetween $\Delta_q$ and $T$. Assuming that every irreducible $T$-module is thin,we display a surjective $\C$-algebra homomorphism $\Delta_q \to T$. This givesa $\Delta_q$ action on the standard module of $T$.

Distance-regular graphs of $q$-Racah type and the universal Askey-Wilson algebra