Mirror construction of Hecke correspondence between Nakajima quiver varieties
Siu-Cheong Lau, Ju Tan
TL;DR
This paper links Hecke correspondences in Nakajima quiver varieties to localized mirror symmetry, demonstrating a new geometric construction and showing the functor's full faithfulness for non-ADE quivers.
Contribution
It introduces a mirror construction for Hecke correspondences and proves the full-faithfulness of the localized mirror functor for non-ADE quivers.
Findings
Hecke correspondences are realized via localized mirror symmetry.
The localized mirror functor is fully faithful for non-ADE quivers.
Provides a new geometric perspective on Nakajima quiver varieties.
Abstract
Nakajima constructed geometric representations of a deformed Kac-Moody Lie algebra using Hecke correspondences between quiver varieties. In this paper, we show that Hecke correspondences, which are holomorphic Lagrangians in products of Nakajima quiver varieties, can be obtained by applying the localized mirror construction to the morphism spaces between families of framed Lagrangian branes supported on the core of a plumbing of two-spheres. Moreover, for a non-ADE quiver, we show that the localized mirror functor is fully-faithful.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology