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

Abstract

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.