Elliptic stable envelopes of affine type $A$ quiver varieties

TL;DR

This paper extends the formula for elliptic stable envelopes from Hilbert schemes to affine type A Nakajima quiver varieties, accommodating various polarizations and chambers, with accompanying computational implementation.

Contribution

It generalizes Smirnov's formula to affine type A quiver varieties with flexible polarization and chamber choices, providing explicit formulas and computational tools.

Findings

Derived explicit formulas for elliptic stable envelopes of affine type A quiver varieties.

Developed a Maple code implementation of the formulas.

Enhanced understanding of stability conditions in quiver varieties.

Abstract

We generalize Smirnov's formula for the elliptic stable envelopes of the Hilbert scheme of points in $\mathbb{C}^2$ to the case of affine type $A$ Nakajima quiver varieties constructed with positive stability condition. We allow for arbitrary choices of polarization and a fairly general choice of chamber. This paper is a companion to the Maple code developed by the author, which implements the formulas described in this paper and is available on the author's website.