Abstract:
In a series of papers beginning in 1975, Margulis classified all finite dimensional representations of lattices in higher rank semisimple Lie groups ([Mar75],[Mar84],[Mar91]). In particular, it was shown that such a representation is always derived from a representation of the whole group. This result is the celebrated Margulis’ superrigidity theorem, and has many striking implications. Most importantly, it implies that lattices in higher rank semisimple Lie groups are always arithmetic groups. In this thesis we give an introduction to the basic theory of lattices and arithmetic groups, and give a proof of the superrigidity theorem.