Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity

TL;DR

This paper investigates the rigidity of smooth factors in the actions of higher rank lattice groups on flag manifolds, demonstrating under certain conditions that these factors are smoothly conjugate to standard actions.

Contribution

It establishes a rigidity result for smooth factors of lattice actions on flag manifolds, extending understanding of their structure under mild differentiability conditions.

Findings

Smooth factors are $C^{ abla}$-conjugate to standard actions

Rigidity holds under mild differentiability sink condition

Extends previous rigidity results to broader class of actions

Abstract

We study smooth factors of the standard actions of lattices in higher rank semisimple Lie groups on flag manifolds. Under a mild condition on existence of a single differentiable sink, we show that these factors are $C^{\infty}$-conjugate to the standard actions on flag manifolds.