Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

Details Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves

2008-09-23

arxiv.org/abs/0809.4010v3

Selecta Math. 16 (2010), no. 16, 201-240

Mathematics

Representation Theory

36 pages; v2: Definition of geometric Heisenberg operators modified; v3: Minor typos corrected

Scientific paper

10.1007/s00029-009-0015-1

We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on the complex projective plane. The top non-vanishing Chern classes of the cohomology of these complexes yield actions of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology of the moduli spaces. In this way we obtain a geometric realization of the boson-fermion correspondence and related vertex operators.

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