论文标题
连贯的滑轮和量子库仑分支II：颤抖的理论和结出同源
Coherent sheaves and quantum Coulomb branches II: quiver gauge theories and knot homology
论文作者
论文摘要
在颤抖的理论的情况下，我们继续研究库仑分支的非交通分辨率。其中包括A型中的Slodowy Slices和$ \ Mathbb {C}^2 $中的对称功率作为特殊情况。这些分辨率基于量子场理论中的涡旋线缺陷，但具有精确的数学描述，在Quiver情况来是KLRW代数的形式主义的修改。虽然在特征性$ p $中依赖于仿生的草个植物和代表理论的几何形状的上下文中得到了最好的理解，但我们对库仑分支及其交换性和非交通分辨率进行了描述，这些分支纯粹可以用代数来理解。 这使我们能够构建使用Aganagić定义的打结同源性理论的纯粹代数版本，并将reshetikhin-turaev不变式分类用于Ade Lie代数类型的微小表示。我们表明，这种同源不变与以前由作者定义的这些不变性的分类，因此与A型中的Khovanov-Rozansky同源性一致。
We continue our study of noncommutative resolutions of Coulomb branches in the case of quiver gauge theories. These include the Slodowy slices in type A and symmetric powers in $\mathbb{C}^2$ as special cases. These resolutions are based on vortex line defects in quantum field theory, but have a precise mathematical description, which in the quiver case is a modification of the formalism of KLRW algebras. While best understood in a context which depends on the geometry of the affine Grassmannian and representation theory in characteristic $p$, we give a description of the Coulomb branches and their commutative and non-commutative resolutions which can be understood purely in terms of algebra. This allows us to construct a purely algebraic version of the knot homology theory defined using string theory by Aganagić, categorifying the Reshetikhin-Turaev invariants for minuscule representations of type ADE Lie algebras. We show that this homological invariant agrees with the categorification of these invariants previously defined by the author, and thus with Khovanov-Rozansky homology in type A.
