Boundaries, Weyl groups, and Superrigidity
Abstract
This note describes a unified approach to several superrigidity results, old and new, concerning representations of lattices into simple algebraic groups over local fields. For an arbitrary group $\Gamma$ and a $\Gamma$boundary $B$ we associate certain generalized Weyl group $W_{\Gamma,B}$ and show that any representation with a Zariski dense unbounded image in a simple algebraic group, $\rho:\Gamma\to \mathbf{H}$, defines a special homomorphism $W_{\Gamma,B}\to {\rm Weyl}(\mathbf{H})$. This general fact allows to deduce the aforementioned superrigidity results.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 DOI:
 10.48550/arXiv.1109.3482
 arXiv:
 arXiv:1109.3482
 Bibcode:
 2011arXiv1109.3482B
 Keywords:

 Mathematics  Group Theory;
 20E40
 EPrint:
 7 pages