Capped vertex with descendants for zero dimensional A∞ quiver varieties

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate the capped vertex functions associated with certain zero-dimensional type -A Nakajima quiver varieties. We derive explicit combinatorial formulas for the capped vertex functions by inserting descendants using the Macdonald operators. We determine the monodromy of the vertex functions and establish its coincidence with the elliptic R-matrix of the symplectic dual variety. We also apply our findings to compute the vertex functions and characters of tautological bundles on quiver varieties formed from arbitrary stability conditions.