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

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Algebraic Geometry

Quantum Algebra

Representation Theory

High Energy Physics - Theory

Mathematical Physics

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.

Authors

Peter Koroteev, Anton M. Zeitlin

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