Nov 2 at 17:30 in 507

Tianqing Zhu

Title:  Stability condition wall-crossing for Nakajima quiver varieties II: Wall-crossing phenomenon for the quantum difference equations 

Abstract: In the previous talk we have shown that  the quantum loop groups of different stability conditions can be related by the wall-crossing auto-equivalence. In this talk we show that the quantum difference operators of Nakajima quiver varieties of different generic stablity conditions are also equivalent up to constant by the wall-crossing auto-equivalences. Moreover using this result, we show that the monodromy representation of the quantum differential equation for the Nakajima quiver variety is equivalent to the mondromy representation constructed by Halpern-Leistner--Sam using the nonabelian stable envelopes.