Representations with minimal support for quantized Gieseker varieties

We study the minimally supported representations of quantizations of Gieseker moduli spaces. We relate them to ${\mathrm{SL}}_n$-equivariant D-modules on the nilpotent cone of ${\mathfrak{s}\mathfrak{l}}_n$ 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.