JMD
New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions
Zhenqi Jenny Wang
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 generators and relations in classical Lie groups rigidity cocycles partial hyperbolicity. Steinberg symbols
JMD
Local rigidity of partially hyperbolic actions
Zhenqi Jenny Wang
We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such actions. The conclusions are based on progress toward computations of the Schur multipliers of these non-split groups, which is the main aim of the second part.
keywords: rigidity cocycles generators and relations in classical Lie groups. Steinberg symbols action of higher rank abelian groups
ERA-MS
Local rigidity of partially hyperbolic actions
Zhenqi Jenny Wang
We prove the local differentiable rigidity of partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. The conclusions are based on geometric Katok-Damjanovic way and progress towards computations of the Schur multipliers of these non-split groups.
keywords: Schur multiplier. Local rigidity group actions

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