Journal of Modern Dynamics (JMD)

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

Pages: 585 - 608, Issue 4, October 2010      doi:10.3934/jmd.2010.4.585

       Abstract        References        Full Text (295.5K)       Related Articles

Zhenqi Jenny Wang - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: 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.

Keywords:  Actions of higher rank abelian groups, cocycles, rigidity, Steinberg symbols, generators and relations in classical Lie groups, partial hyperbolicity.
Mathematics Subject Classification:  Primary: 37D; Secondary: 19C, 22E.

Received: January 2010;      Revised: September 2010;      Available Online: January 2011.