Shuffle products for elliptic stable envelopes of Nakajima varieties

TL;DR

This paper provides an explicit inductive formula for computing elliptic stable envelopes of Nakajima varieties, extending to instanton moduli spaces, based on abelianization techniques.

Contribution

It introduces a novel explicit formula for elliptic stable envelopes of Nakajima varieties, derived via abelianization, and applies it to instanton moduli spaces.

Findings

Explicit formula for elliptic stable envelopes of Nakajima varieties.

Extension of results to instanton moduli spaces.

Connection with Smirnov's formula for Hilbert schemes.

Abstract

We find an explicit formula that produces inductively the elliptic stable envelopes of an arbitrary Nakajima variety associated to a quiver Q from the ones of those Nakajima varieties whose framing vectors are the fundamental vectors of the quiver Q, i.e. the dimension vectors with just one unitary nonzero entry. The result relies on abelianization of stable envelopes. As an application, we combine our result with Smirnov's formula for the elliptic stable envelopes of the Hilbert scheme of points on the plane to produce the elliptic stable envelopes of the instanton moduli space.