  We study the minimally supported representations of quantizations of Gieseker
moduli spaces. We relate them to $\operatorname{SL}_n$-equivariant D-modules on
the nilpotent cone of $\mathfrak{sl}_n$ and to minimally supported
representations of type A rational Cherednik algebras. Our main result is
character formulas for minimally supported representations of quantized
Gieseker moduli spaces.
