Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces

TL;DR

This paper classifies invariant measures on homogeneous spaces under solvable group actions, providing new results for semisimple subgroup actions without characteristic restrictions.

Contribution

It introduces a characteristic-free classification of measures invariant under solvable groups, extending measure rigidity results to broader settings.

Findings

First measure classification for semisimple subgroup actions without characteristic restrictions

Invariant measures characterized for solvable subgroup actions on homogeneous spaces

Independent of characteristic, broadening applicability of measure rigidity

Abstract

We classify measures on a homogeneous space which are invariant under a certain solvable subgroup and ergodic under its unipotent radical. Our treatment is independent of characteristic. As a result we get the first measure classification for the action of semisimple subgroups without any characteristic restriction.