Local Rigidity of Partially Hyperbolic Actions

TL;DR

This paper proves local differentiable rigidity for certain high-rank abelian actions on compact homogeneous spaces and advances understanding of the Schur multipliers of specific non-split groups.

Contribution

It establishes local rigidity results for partially hyperbolic actions and computes Schur multipliers for particular non-split groups, linking dynamical systems and algebraic group theory.

Findings

Proved local differentiable rigidity for high-rank abelian actions.

Computed Schur multipliers for simple indefinite orthogonal and unitary groups.

Connected rigidity phenomena with algebraic properties of non-split groups.

Abstract

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 towards computations of the Schur multipliers of these non-split groups, which is the main aim of the second part.