Pursuing quantum difference equations I: stable envelopes of subvarieties

Abstract

Let X be a symplectic variety equipped with an action of a torus \({\mathsf {A}}\). Let \({\varvec{\nu }}_{b}\subset {\mathsf {A}}\) be a finite cyclic subgroup. We show that K-theoretic stable envelope of the fixed point set \(X^{{\varvec{\nu }}_{b}}\subset X\) can be obtained via a limit of the elliptic stable envelopes of X. An example of X given by the Hilbert scheme of points in the complex plane is considered in detail.