Connections Between Type A Quiver Loci and Positroid Varieties in the Grassmannian

Abstract

In [KR15], it was shown that each type A quiver locus is closely related to a Schubert variety in a partial flag variety. In this thesis, we adapt the construction to show that type A quiver loci are also closely related to positroid varieties in Grassmannians. An important idea in producing this construction is a new combinatorial identification between quiver rank arrays and bounded affine permutations.