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arXiv · 2110.07060

Mixed Hodge structures on character varieties of nilpotent groups

Carlos Florentino·Sean Lawton·Jaime Silva
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Abstract

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.

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Carlos Florentino, Sean Lawton, Jaime Silva. 2021-10-13. Mixed Hodge structures on character varieties of nilpotent groups. https://doi.org/10.1007/s13163-024-00490-9

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