Bow Varieties as Symplectic Reductions of <i>T</i>*(<i>GL</i> <i>n</i>/<i>P</i>)

Abstract Cherkis bow varieties were introduced as ADHM type descriptions of moduli spaces of instantons on the Taub-NUT space equivariant under a cyclic group action. They are also models of Coulomb branches of quiver gauge theories of affine type $A$. In this paper, we realize each bow variety with torus fixed points as a symplectic reduction of a cotangent bundle of a partial flag variety by a unipotent group, and find a slice of this action. By this description, we calculate the equivariant cohomology (and ordinary cohomology) of some of them and answer some questions raised before. This also uses a new result about circle-equivariant cohomology proven in an appendix by Matthias Franz. We also give an explicit generalized Mirkovic–Vybornov isomorphism for bow varieties in the Appendix.