Chevalley-Monk formulas for bow varieties

Abstract: The theory of stable envelopes, introduced by Maulik and Okounkov, provides a fascinating interplay between the geometry of holomorphic symplectic varieties and integrable systems. We apply this theory to bow varieties which form a rich family of holomorphic symplectic varieties including type A Nakajima quiver varieties. We then discuss a formula for the multiplication of torus equivariant first Chern classes of tautological bundles of bow varieties with respect to the stable envelope basis. This formula naturally generalizes the classical Chevalley-Monk formula and can be expressed in terms of moves on skein-type diagrams that label the stable envelope basis.