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Let $\mathbb{K}$ denote an algebraically closed field. Let $V$ denote avector space over $\mathbb{K}$ with finite positive dimension. By a Leonardtriple on $V$ we mean an ordered triple of linear transformations in ${\rmEnd}(V)$ such that for each of these transformations there exists a basis of$V$ with respect to which the matrix representing that transformation isdiagonal and the matrices representing the other two transformations areirreducible tridiagonal. There is a family of Leonard triples said to haveQRacah type. This is the most general type of Leonard triple. We classify theLeonard triples of QRacah type up to isomorphism. We show that any Leonardtriple of QRacah type satisfies the $\mathbb{Z}_3$-symmetric Askey-Wilsonrelations.

The classification of Leonard triples of QRacah type