Differential equations for principal series whittaker functions on SU(2,2)

Let SU(2,2) be the special unitary group of index (2,2). In this paper, two explicit linear partial differential equations are obtained: one from the Casimir operator and the other from the Schmid operator by taking their radial parts. Whittaker functions belonging to an irreducible principal series representation of SU(2,2) satisfy the system of differential equations and furthermore this system becomes holonomic when the dimension of a minimal K-type of the representation is one or two.