Capped vertex with descendants for zero dimensional $A_{\infty}$ quiver varieties

Understand

In this paper, we study the capped vertex functions associated to certain zero-dimensional type-$A$ Nakajima quiver varieties.

• The insertion of descendants into the vertex functions can be expressed by the Macdonald operators, which leads to explicit combinatorial formulas for the capped vertex functions.
• We determine the monodromy of the vertex functions and show that it coincides with the elliptic R-matrix of symplectic dual variety.
• We apply our results to give the vertex functions and the characters of the tautological bundles on the quiver varieties formed from arbitrary stability conditions.