论文标题
基本的单极操作员和kac-moody Aggine Grassmannian片的嵌入
Fundamental monopole operators and embeddings of Kac-Moody affine Grassmannian slices
论文作者
论文摘要
Braverman，Finkelberg和Nakajima将Kac-Moody Aggine Grassmannian Slices定义为$ 3D $ $ $ $ \ MATHCAL {N} = 4 $ QUIVER GAUGE理论的库仑分支，并证明其Coulomb分支结构与有限de类型的通常的Loop Group Construction一致。库仑分支结构具有良好的代数特性，但总体上很难理解其几何形状。 在有限类型中，必不可少的几何特征是切片相互嵌入。我们表明，这些嵌入与基本单极操作员（FMO）兼容，这是由库仑分支结构引起的显着的规则功能。除了有限类型之外，这些嵌入尚不清楚，我们的第二个结果是为所有对称的Kac-Moody类型构建它们。我们表明，这些嵌入在温和的“善良”假设下尊重泊松结构。这些结果对Finkelberg在其2018年ICM讲话中提出的一个问题提供了肯定的答案，并证明了FMO在研究Kac-Moody Aggine Grassmannian Slices的几何形状时的实用性，即使在有限类型中也是如此。
Braverman, Finkelberg, and Nakajima define Kac-Moody affine Grassmannian slices as Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and prove that their Coulomb branch construction agrees with the usual loop group definition in finite ADE types. The Coulomb branch construction has good algebraic properties, but its geometry is hard to understand in general. In finite types, an essential geometric feature is that slices embed into one another. We show that these embeddings are compatible with the fundamental monopole operators (FMOs), remarkable regular functions arising from the Coulomb branch construction. Beyond finite type these embeddings were not known, and our second result is to construct them for all symmetric Kac-Moody types. We show that these embeddings respect Poisson structures under a mild "goodness" hypothesis. These results give an affirmative answer to a question posed by Finkelberg in his 2018 ICM address and demonstrate the utility of FMOs in studying the geometry of Kac-Moody affine Grassmannian slices, even in finite types.
