Boundaries, Weyl groups, and Superrigidity
journal contributionposted on 2012-08-17, 00:00 authored by Uri Bader, Alex Furman
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 Γ and a boundary action Γ B we associate a certain generalized Weyl group WΓ,B and show that any representation with a Zariski dense unbounded image in a simple algebraic group, ρ : Γ → H, defines a special homomorphism WΓ,B → WeylH. This general fact allows the deduction of the aforementioned superrigidity results.
U.B. and A.F. were supported in part by the BSF grant 2008267. U.B was supported in part by the ISF grant 704/08. A.F. was supported in part by the NSF grants DMS 0905977.
Publisher Statement© 2012 by American Institute of Mathematical Sciences, Electronic Research Announcements DOI: 10.3934/era.2012.19.41
PublisherAmerican Institute of Mathematical Sciences