On Fuchsian loci of PSL(n,R)-Hitchin components of a pair of pants

TL;DR

This paper explicitly parametrizes the Fuchsian loci within PSL(n,R)-Hitchin components for a pair of pants using Bonahon-Dreyer coordinates, advancing understanding of these geometric structures.

Contribution

It provides the first explicit parametrization of Fuchsian loci in PSL(n,R)-Hitchin components for a pair of pants, utilizing Bonahon-Dreyer coordinates.

Findings

Explicit parametrization of Fuchsian loci achieved

Enhanced understanding of PSL(n,R)-Hitchin components

Application of Bonahon-Dreyer parametrization to Fuchsian loci

Abstract

In this paper, we study Fuchsian loci of ${\rm PSL}_n(\mathbb{R})$-Hitchin components. In particular, using the Bonahon-Dreyer parametrization of ${\rm PSL}_n(\mathbb{R})$-Hitchin components, we give an explicit parametrization of Fuchsian loci of a pair of pants.