Commuting elements in reductive groups and Higgs bundles on abelian varieties
Algebraic Geometry
2021-05-25 v1
Abstract
Let G be a connected real reductive algebraic group, and let K be a maximal compact subgroup of G. We prove that the conjugation orbit space Hom(Z^{2d},K)/K is a strong deformation retract of the space Hom(Z^{2d},G)/G of equivalence classes of representations of Z^{2d} into G. This is proved by showing that the homotopy type of the moduli space of principal G-Higgs bundles of vanishing rational characteristic classes on a complex abelian variety of dimension d depends only on K.
Cite
@article{arxiv.1305.3429,
title = {Commuting elements in reductive groups and Higgs bundles on abelian varieties},
author = {Indranil Biswas and Carlos Florentino},
journal= {arXiv preprint arXiv:1305.3429},
year = {2021}
}