$Q$-polynomial distance-regular graphs and a double affine Hecke algebra of rank one

Understand

We study a relationship between $Q$-polynomial distance-regular graphs and the double affine Hecke algebra of type $(C^{\vee}_1,C_1)$.

• Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with vertex set $X$.
• We assume that $\Gamma$ has $q$-Racah type and contains a Delsarte clique $C$.
• Fix a vertex $x \in C$.