  The main purpose of this paper is to obtain an explicit expression of a
family of matrix valued orthogonal polynomials {P_n}_n, with respect to a
weight W, that are eigenfunctions of a second order differential operator D.
The weight W and the differential operator D were found in [12], using some
aspects of the theory of the spherical functions associated to the complex
projective spaces. We also find other second order differential operator E
symmetric with respect to W and we describe the algebra generated by D and E.
