$\Theta$-positive representations over real closed fields

TL;DR

This paper introduces a broad framework for $ heta$-positive representations over real closed fields, extending existing concepts of positive and Anosov representations without requiring boundary map continuity.

Contribution

It generalizes the theory of positive representations to real closed fields and removes the continuity assumption on boundary maps.

Findings

Defines $ heta$-positive representations over real closed fields

Encompasses various known positive and Anosov representations

Provides a unified theoretical framework

Abstract

We develop the theory of $\Theta$-positive representations from general Fuchsian groups to linear groups over real closed fields. Our definition, which does not assume the boundary map to be continuous, encompasses many generalizations of positive or Anosov representations that have been considered in the literature.