A geometric boson-fermion correspondence
Alistair Savage
Abstract
The fixed points of a natural torus action on the Hilbert schemes of points in C2 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.
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