Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}

Details Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)} Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}

2006-07-26

arxiv.org/abs/math/0607690v1

Mathematics

Representation Theory

32 pages

Scientific paper

We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP^2. Using these constructions, we realize geometrically all level one irreducible representations of the affine Lie algebra \hat{gl(r)}. The cyclic group Z_k acts naturally on the moduli space of sheaves, and the fixed-point components of this action are cyclic Nakajima quiver varieties . We realize level k irreducible representations of \hat{gl(r)} on the equivariant cohomology of these quiver varieties.

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