arXiv 1706.021122017-06math.RThep-thmath-phmath.AGmath.DGmath.MP

源自 Coulomb 分支的等变导出 Satake 范畴中的环对象（附 Gus Lonergan 撰写的附录）

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

Alexander Braverman, Michael Finkelberg, Hiraku Nakajima

备注：: 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
发表信息：: Adv. in Theo. and Math. Physics 23 (2019) No.2, 253-344; Errata: Adv. in Theo. and Math. Physics 25 (2021), No.4, 957--992

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AI总结：

本文证明三元组簇到仿射 Grassmannian 态射的对偶化复形正像构成等变导出 Satake 范畴中的环对象，并将既有构造推广到任意交换环对象，同时研究星形箭图对应的 Coulomb 分支。

摘要：

这是 arXiv:1601.03586 的第二篇配套论文。我们考察从 arXiv:1601.03586 中引入的三元组簇到仿射 Grassmannian 的态射。对偶化复形的正像在仿射 Grassmannian 上的等变导出范畴（即等变导出 Satake 范畴）中是一个环对象。我们证明 arXiv:1601.03586 中的各种构造对任意交换环对象均有效。本文的第二个目的是研究与星形箭图相关的 Coulomb 分支；根据 arXiv:1007.0992，这些分支被预期为 A 型三维 Sicilian 理论的猜想性 Higgs 分支。

英文摘要：

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.

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