A-type Quiver Varieties and ADHM Moduli Spaces

Abstract

We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with a nontrivial match between their equivariant parameters. In particular, we demonstrate that quantum equivariant K-theory of $A_n$ quiver varieties in a certain $n\to \infty$ limit reproduces equivariant K-theory of the Hilbert scheme of points on ${\mathbb{C}}^2$. We analyze the correspondence from the point of view of enumerative geometry, representation theory and integrable systems. We also propose a conjecture which relates spectra of quantum multiplication operators in K-theory of the ADHM moduli spaces with the solution of the elliptic Ruijsenaars-Schneider model.

31 pages, 3 figures, to appear in Communications in Mathematical Physics

References in corpus (1)

• Defects and Quantum Seiberg-Witten Geometry

Cited by in corpus (5)

• 3d Mirror Symmetry for Instanton Moduli Spaces
• Toroidal q-Opers
• Double Inozemtsev Limits of the Quantum DELL System
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Quantum K-theory and Integrability