Let D be a bounded symmetric domain. Let G be the universal covering group of the identity component A 0 ( D ) {A_0}(D) of the group of all holomorphic diffeomorphisms of D onto itself. In this case, any G-homogeneous vector bundle E → D E \to D admits a natural structure of G-homogeneous holomorphic vector bundles. The vector bundle E → D E \to D must be holomorphically trivial, since D is a Stein manifold. We exhibit explicitly a holomorphic trivialization of E → D E \to D by defining a map Φ : G → GL ( V ) \Phi :G \to {\text {GL}}(V) (V being the fiber of the vector bundle) which extends the classical “universal factor of automorphy” for the action of A 0 ( D ) {A_0}(D) on D. Then, we study the space H of all square integrable holomorphic sections of E → D E \to D . The natural action of G on H defines a unitary irreducible representation of G. The representations obtained in this way are square integrable over G / Z G/Z (Z denotes the center of G) in the sense that the absolute values of their matrix coefficients are in L 2 ( G / Z ) {L_2}(G/Z) .