Maximal and Borel Anosov representations in $Sp(4,\mathbb{R})$

TL;DR

This paper characterizes certain surface group representations into Sp(4,R), showing that maximal Borel Anosov representations are Hitchin and linking maximality to hyperconvexity in Sp(2n,R).

Contribution

It establishes a classification of maximal Borel Anosov representations in Sp(4,R) and relates maximality to hyperconvexity in higher rank symplectic groups.

Findings

Maximal Borel Anosov representations in Sp(4,R) are Hitchin.

Maximality in Sp(2n,R) with n-1,n Anosov representations is characterized by hyperconvexity.

The paper provides a criterion for maximality based on geometric properties.

Abstract

We prove that any Borel Anosov representations of a surface group into $Sp(4,\mathbb{R})$ that has maximal Toledo invariant must be Hitchin. We also prove that a representation of a surface group into $Sp(2n,\mathbb{R})$ that is $\{n-1,n\}$-Anosov is maximal if and only if it satisfies the hyperconvexity property $H_n$.