Topological mirror symmetry for parabolic Higgs bundles

TL;DR

This paper proves the topological mirror symmetry conjecture for moduli spaces of strongly parabolic Higgs bundles of rank two and three, with broader results for prime ranks, advancing understanding in geometric representation theory.

Contribution

It establishes the topological mirror symmetry for specific moduli spaces of parabolic Higgs bundles, extending previous conjectures and results to rank three and prime ranks.

Findings

Proves topological mirror symmetry for rank 2 and 3 Higgs bundles.

Extends results to any prime rank for most cases.

Advances the understanding of moduli spaces in geometric representation theory.

Abstract

We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank.