Title: Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan),
Abstract: This is the second companion paper of arXiv:1601.03586. We consider the
morphism from the variety of triples introduced in arXiv:1601.03586 to the
affine Grassmannian. The direct image of the dualizing complex is a ring object
in the equivariant derived category on the affine Grassmannian (equivariant
derived Satake category). We show that various constructions in
arXiv:1601.03586 work for an arbitrary commutative ring object.
The second purpose of this paper is to study Coulomb branches associated with
star shaped quivers, which are expected to be conjectural Higgs branches of
$3d$ Sicilian theories in type $A$ by arXiv:1007.0992.