Lemay, Joel2015-09-182015-09-1820152015http://hdl.handle.net/10393/32866http://dx.doi.org/10.20381/ruor-4140The 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.enLie AlgebraQuiver VarietyAlgebraic GeometryEquivariant CohomologyGeometric Invariant TheoryRepresentation TheoryThesis