Hypercubes, Leonard triples and the anticommutator spin algebra

Understand

This paper is about three classes of objects: Leonard triples, distance-regular graphs and the modules for the anticommutator spin algebra.

• Let $\K$ denote an algebraically closed field of characteristic zero.
• Let $V$ denote a vector space over $\K$ with finite positive dimension.
• A Leonard triple on $V$ is an ordered triple of linear transformations in $\mathrm{End}(V)$ such that for each of these transformations there exists a basis for $V$ with respect to which the matrix representing that transformation is diagonal and the matrices representing the other two transformations are irreducible tridiagonal.