The Cayley–Laplace differential operator on the space of rectangular matrices

This paper deals with the homogeneous Cayley–Laplace differential operator on the space of rectangular real matrices. Using Riesz potentials, we obtain fundamental solutions for this operator and some of its powers. We establish that the Cayley–Laplace operator satisfies the strong Huygens principle. Using intertwining operators with spectral parameters, we consider deformations of the Cayley–Laplace operator and find sufficient conditions under which these deformations satisfy the strong Huygens principle.