Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups

Ruoxi Li; Rahul Singh

Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups

Algebraic Geometry 2024-11-11 v2

Authors: Ruoxi Li , Rahul Singh

Abstract

Let $Hom^0(\Gamma,G)$ be the path-connected component of the identity representation of the variety of representations of a finitely generated nilpotent group $\Gamma$ into a connected reductive complex affine algebraic group $G$ . With the formulas given by Florentino, Lawton and Silva, we provide explicit partition type formulas for the mixed Hodge polynomials of character varieties $Hom^0(\Gamma,G)// G$ when $G=Sp_{2n}$ and $G=SO_{n}$ .

Keywords

mixed Hodge polynomials character varieties nilpotent groups explicit formulas partition type formulas

Cite

@article{arxiv.2410.10008,
  title  = {Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups},
  author = {Ruoxi Li and Rahul Singh},
  journal= {arXiv preprint arXiv:2410.10008},
  year   = {2024}
}

Comments

A mistake in the previous version of the article is corrected (see Fact 2.2) and this version generalizes to finitely generated nilpotent groups of positive abelian rank

Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups

Abstract

Keywords

Cite

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