On the existence of infinite series of exotic holonomies

In 1955, Berger [Ber] gave a list of irreducible reductive representations which can occur as the holonomy of a torsion-free affine connection. While this list was stated to be complete in the case of metric connections, the situation in the general case remained unclear. The representations which are missing from this list are called exotic. In this paper, we use twistor techniques to detect an infinite series of candidates for exotic holonomies. We then develop a general method for constructing torsion-free affine connections with prescribed holonomy which is based onequivariant deformations of a certain class of linear Poisson structures. When applied to the new series, this method yields an exhaustive description of all torsion-free connections with these holonomies, and hence not only proves the existence of such connections, but also allows us to deduce some striking facts about their local and global behaviour.