Local Rigidity of Higher Rank Homogeneous Abelian Actions: a Complete Solution via the Geometric Method

Kurt Vinhage, Zhenqi Jenny Wang

Published 2015-10-03Version 1

We show smooth local rigidity for most abelian higher-rank partially hyperbolic algebraic actions on homogeneous spaces obtained from semisimple Lie groups as well as their semidirect with vector spaces. The method of proof is a combination of geometric method and algebraic computation toward Schur multipliers. The principal difference with previous work that used similar methods is the very general nature of our proofs. It is also the first time that partially hyperbolic twisted symmetric space examples have been treated from literature.