Measures Invariant Under Horospherical Subgroups in Positive characteristic

TL;DR

This paper establishes measure rigidity results for horospherical subgroup actions on homogeneous spaces over fields of positive characteristic, extending understanding of dynamical systems in this setting.

Contribution

It proves measure rigidity for horospherical subgroup actions on homogeneous spaces over positive characteristic fields, a novel extension of existing rigidity theories.

Findings

Measure rigidity for horospherical actions in positive characteristic.

Applicable to homogeneous spaces from arithmetic lattices.

Advances understanding of dynamics in positive characteristic settings.

Abstract

We prove measure rigidity for the action of (maximal) horospherical subgroups on homogeneous spaces obtained by quotient by a uniform (nonuniform) arithmetic lattices over a field of positive characteristic.