Pursuing quantum difference equations I: stable envelopes of subvarieties

Abstract

Let $X$ be a symplectic variety equipped with an action of a torus $A$. Let $\nu \subset A$ be a finite cyclic subgroup. We show that K-theoretic stable envelope of subvarieties $X^{\nu}\subset X$ can be obtained via various limits 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 details.