A formula for non-equioriented quiver orbits of type A

Abstract

We prove a positive combinatorial formula for the equivariant class of an orbit closure in the space of representations of an arbitrary quiver of type $A$. Our formula expresses this class as a sum of products of Schubert polynomials indexed by a generalization of the minimal lace diagrams of Knutson, Miller, and Shimozono. The proof is based on the interpolation method of Feh\'er and Rim\'anyi. We also conjecture a more general formula for the equivariant Grothendieck class of an orbit closure.