Abstract: Let V be a finite dimensional vector space over a field K. Let A and A^* be linear transformations from V to V. We say A, A^* is a tridiagonal pair whenever (i) A, A^* are both diagonalizable (ii) A and A^* act tridiagonally on each others' eigenspaces and (iii) the only proper subspace of V that is invariant under A and A^* is the zero subspace. We say A, A^* is a Leonard pair whenever A, A^* is a tridiagonal pair and the dimensions of all the eigenspaces of both A and A^* are 1. In this talk we introduce the associativeK-algebra $\Box_q$ and discuss how tridiagonal pairs and Leonard pairs are related to $Box_q$-modules.