Positive representations over real closed fields

Abstract

We develop the theory of $\hat{I}˜$-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.

106 pages. Added a conjecture on flag varieties with a positive structure (Conjecture 1.6), proved this conjecture in some cases (Section 3.9) and improved some theorems conditionally to this conjecture (Theorem H, Section 4.6, Corollary 7.5)