Hypercube and tetrahedron algebra.

Let D be an integer at least 3 and let H( D, 2) denote the hypercube. It is known that H( D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all { D − 2 i}, Suppose that ⊠ denotes the tetrahedron algebra. In this paper, the authors display an action of ⊠ on the standard module V of H( D, 2). To describe this action, the authors define six matrices in Mat(ℂ), called Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ⊠ on V. [ABSTRACT FROM AUTHOR]