Heisenberg categorification and Hilbert schemes

Abstract

Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on Hilbert schemes of points on the minimal resolutions of C^2/G.

53 pages

References in corpus (4)

• 2-Kac-Moody algebras
• Hecke algebras, finite general linear groups, and Heisenberg categorification
• Vertex operators and 2-representations of quantum affine algebras
• Heisenberg algebra and a graphical calculus

Cited by in corpus (32)

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• Etingof conjecture for quantized quiver varieties
• Hecke algebras, finite general linear groups, and Heisenberg categorification
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• A general approach to Heisenberg categorification via wreath product algebras
• Vertex operators and 2-representations of quantum affine algebras
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Frobenius Heisenberg categorification
• Affine wreath product algebras
• A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)
• Rigidity in higher representation theory
• On a categorical Boson-Fermion correspondence
• Categorification and Heisenberg doubles arising from towers of algebras
• Braid group actions via categorified Heisenberg complexes
• Foundations of Frobenius Heisenberg categories
• A graphical calculus for the Jack inner product on symmetric functions
• W-algebras from Heisenberg categories
• Towers of graded superalgebras categorify the twisted Heisenberg double
• Loop realizations of quantum affine algebras
• Twisted Heisenberg doubles
• A Categorical Quantum Toroidal Action on Hilbert Schemes
• Quantum affine wreath algebras
• A diagrammatic categorification of the fermion algebra
• Representation theory of 0-Hecke-Clifford algebras
• Skew-Zigzag Algebras
• Cluster algebra structure on the finite dimensional representations of $U_q(\widehat{A_3})$ for $l$=2
• Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
• A groupoidification of the fermion algebra
• Planar algebras for the Young graph and the Khovanov Heisenberg category
• Symmetric functions and Springer representations
• Frobenius W-algebras and traces of Frobenius Heisenberg categories