Framed Rank r Torsion-free Sheaves on CP² and Representations of the Affine Lie Algebra gl(r)

2006/07/26 by Anthony Licata, Licata, Anthony
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0607690

32 pages

arxiv created 2006/07/26 · arxiv updated 2009/12/01

Abstract

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 CP². Using these constructions, we realize geometrically all level one irreducible representations of the affine Lie algebra 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 gl(r) on the equivariant cohomology of these quiver varieties.

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