Quantum Springer conjecture for strongly equivariant quantum character modules

Let $G$) be a connected reductive group, let $W$ be its Weyl group, and let $\rho$ denote the relevant quantum Springer constructions appearing in the isomorphism and theorems cited in the source. Quantum Springer conjecture. The isomorphism and the results of the cited Springer theorems all hold for $G$, with the symmetric group ${\operatorname{Sym}}_{N}$ replaced by the Weyl group $W$ of $G$. Proving this requires a theory of $\mathtt{q}$-deformed Springer theory beyond type $A$, where elliptic Schur–Weyl duality is unavailable.