Higgs bundles, pseudo-hyperbolic geometry and maximal representations

TL;DR

This paper explores the interplay between Higgs bundle theory and pseudo-hyperbolic geometry in understanding maximal representations into rank 2 Hermitian Lie groups, revealing new geometric insights.

Contribution

It introduces a novel approach combining Higgs bundles and pseudo-hyperbolic geometry to analyze maximal representations into specific Lie groups.

Findings

Establishes connections between Higgs bundles and pseudo-hyperbolic geometry.

Provides new geometric characterizations of maximal representations.

Enhances understanding of representations into rank 2 Hermitian Lie groups.

Abstract

These notes are an extended version of a talk given by the author in the seminar "Theorie Spectrale et Geometrie" at the Institut Fourier in No- vember 2016. We present here some aspects of a work in collaboration with B. Collier and N. Tholozan (arXiv:1702.08799). We describe how Higgs bundle theory and pseudo-hyperbolic geometry interfere in the study of maximal representations into Hermitian Lie groups of rank 2.