On the vertex functions of type A quiver varieties

TL;DR

This paper investigates the quasimap vertex functions of type A Nakajima quiver varieties, providing explicit embeddings and demonstrating the preservation of vertex functions under these embeddings.

Contribution

It constructs explicit embeddings of type A quiver varieties into a standard form and proves the preservation of vertex functions in equivariant K-theory.

Findings

Explicit embedding of any type A quiver variety into a standard form

Preservation of vertex functions under the embedding in equivariant K-theory

Enhanced understanding of quasimap counts for type A quiver varieties

Abstract

The goal of this paper is to better understand the quasimap vertex functions of type $A$ Nakajima quiver varieties. To that end, we construct an explicit embedding of any type $A$ quiver variety into a type $A$ quiver variety with all framings at the rightmost vertex of the quiver. Then we consider quasimap counts, showing that the map induced by this embedding on equivariant $K$-theory preserves vertex functions.