Geometric Realizations of the Basic Representation of the Affine General Linear Lie Algebra

Abstract

The realizations of the basic representation of the affine general linear Lie algebra on (r x r) matrices are well-known to be parametrized by partitions of r and have an explicit description in terms of vertex operators on the bosonic/fermionic Fock space. In this thesis, we give a geometric interpretation of these realizations in terms of geometric operators acting on the equivariant cohomology of certain Nakajima quiver varieties.