Capped vertex with descendants for zero dimensional \(A_\infty\) quiver varieties (Q2131771)

H. Dinkins and A. Smirnov investigate certain \(K\)-theoretic enumerative invariants of Nakajima quiver varieties known as vertex functions. These vertex functions appear as capped and uncapped. The capped vertex functions are associated to certain zero-dimensional type \(A\) Nakajima quiver varieties. In such cases, there are procedures for computing the vertex functions as a power series in the Kähler parameters. 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. The authors determine the monodromy of the vertex functions and show that it coincides with the elliptic \(R\)-matrix of symplectic dual variety. They then apply their results to give the vertex functions and the characters of the tautological bundles on the quiver varieties formed from various stability conditions.