Hyperbolic representations of PU(1,n)

The work is about the study of group representations in the group of isometries of a separable complex hyperbolic space. The main part is the classification of the representations of the group of isometries of a finite dimensional complex hyperbolic space that preserve the type (parabolic, elliptic and hyperbolic) and that are irreducible in the hyperbolic sense. Also the relation between these representations and the functions of hyperbolic type defined by Nicolas Monod.