Carlos Florentino,
Sean Lawton,
Jaime Silva
Character varieties and holomorphic bundles
Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety R and on the character variety R//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.
2022
Florentino, Carlos, Sean Lawton and Jaime Silva. “Mixed Hodge structures on character varieties of nilpotent groups.” arXiv:2110.07060