# Diagonal actions in positive characteristic

## TL;DR

This paper extends measure rigidity theorems to positive characteristic settings, classifying measures and joinings for higher rank actions on algebraic groups over fields of positive characteristic.

## Contribution

It provides the first classification results for positive entropy measures and joinings in positive characteristic, paralleling known results in characteristic zero.

## Key findings

- Classification of positive entropy measures on quotients of SL_d in positive characteristic
- Classification of joinings for higher rank actions on certain algebraic groups
- Extension of measure rigidity theorems to positive characteristic contexts

## Abstract

We prove positive characteristic analogues of certain measure rigidity theorems in characteristic zero. More specifically we give a classification result for positive entropy measures on quotients of $\operatorname{SL}_d$ and a classification of joinings for higher rank actions on simply connected absolutely almost simple groups.