Geometric Realizations of the Basic Representation of $\widehat\mathfrak{gl}_r$
Algebraic Geometry
2014-10-23 v1 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1410.2932,
title = {Geometric Realizations of the Basic Representation of $\widehat\mathfrak{gl}_r$},
author = {Joel Lemay},
journal= {arXiv preprint arXiv:1410.2932},
year = {2014}
}