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

Abstract

Let $Ho{m}^0(\Gamma ,G)$ 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 $Ho{m}^0(\Gamma ,G)//G$ when $G=S{p}_{2n}$ and $G=S{O}_n$.

arXiv commentA 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