Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups

Plethystic exponential calculus and characteristic polynomials of permutations

“…an identity first obtained in the study of symmetric products of algebraic groups (in the case r, s > 0, see [Si,Lem. 4.2]), but here shown for arbitrary r ∈ .…”

Generating series for the E‐polynomials of GL(n,C)$GL(n,{\mathbb {C}})$‐character varieties

“…Proof It follows from a formula of Cheah [3] that symmetric products of balanced varieties are balanced (see also [28]). Therefore, since $$$$\begin{equation*} \mathcal {X}_{\Gamma }^{[1^{n}]}GL_{n}\cong \operatorname{Sym}^{n}\mathcal {X}_{\Gamma }GL_{1}, \end{equation*}$$$$we only need to show that $$\mathcal {X}_{\Gamma }GL_{1}$$ is of Hodge–Tate type.…”

“…This is a consequence of the analogous isomorphism of polystable loci: Proof. It follows from a formula of Cheah [3] that symmetric products of balanced varieties are balanced (see also [28]). Therefore, since…”