A categorical action on quantized quiver varieties

Abstract

In this paper, we describe a categorical action of any Kac-Moody algebra on a category of quantized coherent sheaves on Nakajima quiver varieties. By "quantized coherent sheaves," we mean a category of sheaves of modules over a deformation quantization of the natural symplectic structure on quiver varieties. This action is a direct categorification of the geometric construction of universal enveloping algebras by Nakajima.

26 pages. DVI may not compile correctly; PDF is recommended. v3: extensive rewriting of proofs and exposition; main results are unchanged

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Cited by in corpus (10)

• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Quantizations of conical symplectic resolutions I: local and global structure
• Canonical bases and higher representation theory
• Etingof conjecture for quantized quiver varieties
• Current algebras and categorified quantum groups
• Centers of KLR algebras and cohomology rings of quiver varieties
• Geometry and categorification
• An equivalence between truncations of categorified quantum groups and Heisenberg categories
• Associated graded of Hodge modules and categorical sl_2 actions
• Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]