Bow varieties as symplectic reductions of $T^*(G/P)$

Abstract: Cherkis bow varieties were introduced as ADHM type description of moduli space 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 raisedbefore. This also uses a new result about circle-equivariant cohomology proven in an appendix. We also give an explicit generalized Mirkovic-Vybornov isomorphism for bow varieties in the appendix.