A geometric boson-fermion correspondence

Abstract

The fixed points of a natural torus action on the Hilbert schemes of points in C^2 are quiver varieties of infinite type A. The equivariant cohomology of the Hilbert schemes and quiver varieties can be given the structure of bosonic and fermionic Fock spaces respectively. Then the localization theorem, which relates the equivariant cohomology of a space with that of its fixed point set, yields a geometric realization of the important boson-fermion correspondence.

17 pages; v2: Reference added; v3: Significant expository revision; v4: Small compilation error corrected

References in corpus (3)

• Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics
• Quiver varieties and Hilbert schemes
• A Geometric Realization of Spin Representations and Young diagrams from Quiver Varieties

Cited by in corpus (3)

• Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}
• The combinatorics of ${\mathbb{C}}^{\ast }$-fixed points in generalized Calogero-Moser spaces and Hilbert schemes
• An equivalence between truncations of categorified quantum groups and Heisenberg categories