Geometric Realizations of the Basic Representation of   $\widehat\mathfrak{gl}_r$
  The realizations of the basic representation of $\widehat\mathfrak{gl}_r$ are 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 paper, we give a geometric interpretation of these realizations in terms of geometric operators acting on the equivariant cohomology of certain Nakajima quiver varieties. 
Joel Lemay
math.AG math.RT