Agenda de l’IDP

C*-académie

Théorème de super-rigidité de Margulis : suite
Indira Chatterji
Friday 30 October 2009 14:00 -  Orléans -  Salle de Séminaire

Résumé :
Arithmeticity turned out to be closely related to another remarkable property of lattices discovered by Margulis. Superrigidity for a lattice Γ in G roughly means that any homomorphism of Γ into the group of real invertible n × n matrices extends to the whole G. The name derives from the following variant: If G and G' , semisimple algebraic groups over a local field without compact factors and whose split rank is at least two and Γ and Γ' are irreducible lattices in them, then any homomorphism f: Γ → Γ' between the lattices agrees on a finite index subgroup of Γ with a homomorphism between the algebraic groups themselves. (The case when f is an isomorphism is known as the strong rigidity.) While certain rigidity phenomena had already been known, the approach of Margulis was at the same time novel, powerful, and very elegant.

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