The Hilbert scheme of points on is self-dual under three-dimensional mirror symmetry

3d Mirror Symmetry for Instanton Moduli Spaces

We prove that the moduli spaces of torsion-free sheaves on are self-dual under three-dimensional mirror symmetry using methods of geometry and integrability.In particular, we demonstrate that the corresponding quantum equivariant k-theory is invariant upon interchanging its k\"ahler and equivariant parameters as well as inverting the weight of the first, we find a two-parameter family of self-mirror quiver varieties of type a and study their quantum k-theory algebras via direct limit and by imposing certain periodic boundary conditions on the quiver data.