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

Paul Terwilliger, Arjana Žitnik

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 and relations in the following way. The…