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

Let $Ho{m}^0(\mathrm{\Gamma },G)$ be the path-connected component of the identity representation of the variety of representations of a finitely generated nilpotent group $\mathrm{\Gamma }$ 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 $Ho{m}^0(\mathrm{\Gamma },G)\mathrm{/}\mathrm{/}G$ when $G=S{p}_{2n}$ and $G=S{O}_n$.