qKZ/tRS Duality via Quantum K-Theoretic Counts

Exotic Quantum Difference Equations and Integral Solutions

One of the fundamental objects in the $K$-theoretic enumerative geometry of Nakajima quiver varieties is known as the the capping operator. It is uniquely determined as the fundamental solution to a system of $q$-difference equations. Such difference equations involve shifts of two sets of variables, the variables arising as equivariant parameters for a torus that acts on the variety and an additional set of variables known as Kähler parameters. The difference equations in the former variables were identified with the qKZ equations in [28]. The difference equations in the latter variables were…