Coherent Sheaves on Quiver Varieties and Categorification
Sabin Cautis, Joel Kamnitzer, Anthony Licata
TL;DR
This paper develops geometric categorical actions of Lie algebras on derived categories of coherent sheaves on Nakajima quiver varieties, providing a categorification of algebraic representations and introducing affine braid group actions.
Contribution
It constructs geometric categorical Lie algebra actions on derived categories of Nakajima quiver varieties, advancing the categorification of Kac-Moody algebra representations.
Findings
Categorical Lie algebra actions on derived categories
Categorification of Kac-Moody algebra representations
Affine braid group actions on quiver varieties
Abstract
We construct geometric categorical Lie algebra actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima's construction of Kac-Moody algebra representations on the K-theory of quiver varieties. We define an induced affine braid group action on these derived categories.
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