# American Institute of Mathematical Sciences

October  2010, 4(4): 585-608. doi: 10.3934/jmd.2010.4.585

## New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions

 1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Received  January 2010 Revised  September 2010 Published  January 2011

We prove the local differentiable rigidity of generic partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from split symplectic Lie groups. We also give examples of rigidity for nongeneric actions on compact homogeneous spaces obtained from SL$(2n,\RR)$ or SL$(2n,\CC)$. The conclusions are based on the geometric approach by Katok--Damjanovic and a progress towards computations of the generating relations in these groups.
Citation: Zhenqi Jenny Wang. New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions. Journal of Modern Dynamics, 2010, 4 (4) : 585-608. doi: 10.3934/jmd.2010.4.585
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