The Weyl group and rigidity of group actions.

I will report on a joint work with Alex Furman.
I will explain how one uses the Weyl group of an ambient Lie group in
order to control the actions of its lattices.
In fact one can define a Weyl group even for an abstract group. Most
of the time it will be a boring group consisting of no more than two
elements. If this is not the case, we are likely to encounter some
rigidity phenomena. A standing example (besides higher rank lattices)
are lattices in product of groups.