Shuffle products for elliptic stable envelopes of Nakajima varieties

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.