English

Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)

Representation Theory 2024-01-23 v6 High Energy Physics - Theory Mathematical Physics Algebraic Geometry Differential Geometry math.MP

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 3d3d Sicilian theories in type AA by arXiv:1007.0992.

Keywords

Cite

@article{arxiv.1706.02112,
  title  = {Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)},
  author = {Alexander Braverman and Michael Finkelberg and Hiraku Nakajima},
  journal= {arXiv preprint arXiv:1706.02112},
  year   = {2024}
}

Comments

38 pages; v2. 66 pages, proofs in some results in Sec.5 are corrected. A new appendix by Gus Lonergan on a new proof of the commutativity of the convolution product; v3. the appendix is mentioned in the title; v4. A remark (5.22) on quantization of results in Sect.5 is added; v5. the definition of $\mathcal{S}_N^\circ$ is added; v6. Errata