Instanton moduli space, stable envelopes and quantum difference equations

Abstract

In this article we prove the degeneration limit of the quantum difference equations of instanton moduli space for both algebraic one and the Okounkov-Smirnov geometric one is the Dubrovin connection for the instanton moduli space. As an application, we prove that the Maulik-Okounkov quantum algebra of Jordan type is isomorphic to the quantum toroidal algebra $U_{q_1,q_2}(\hat{\hat{\mathfrak{gl}}}_1)$ up to some centres.