Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra (Q1024879)

In a previous paper [Eur. J. Comb. 30, No.\,3, 682--697 (2009; Zbl 1193.17008)], the authors constructed a representation of the \(q\)-tetrahedron algebra on the standard module of a distance regular graph. In the present paper, they construct a representation using a distance-regular graph having \(q\)-Racah type, with the condition that each irreducible module for a subconstituent algebra is thin. This partly settles a conjecture given in the previous paper.