A geometric boson-fermion correspondence

Details A geometric boson-fermion correspondence A geometric boson-fermion correspondence

2005-08-23

arxiv.org/abs/math/0508438v4

Compt.Rend.Math.Acad.Sci.Canada 28:65-84,2006

Mathematics

Representation Theory

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

Scientific paper

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.

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