论文标题
BFN Springer理论
BFN Springer Theory
论文作者
论文摘要
鉴于n的代表n，braverman-finkelberg-nakajima定义了一个出色的泊松品种，称为库仑分支。他们对这个空间的建设是由3D量规理论和符号双重性的考虑因素激励的。该库仑分支的坐标环被定义为卷积代数，使用G。 该矢量捆绑在仿生的grassmannian地图上，到代表中的循环空间。我们使用这些BFN弹簧纤维来构建（量化的）库仑分支代数的模块。这些模块自然对应于相应仪表理论的边界条件。 我们利用我们的构造部分证明了鲍曼 - 卡姆尼策 - 克诺森的猜想，并为hikita，nakajima和Kamnitzer-McBreen-Proudfoot提供了猜想的证据。我们还证明了BFN Springer纤维与准空间之间的关系。
Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space was motivated by considerations from 3d gauge theories and symplectic duality. The coordinate ring of this Coulomb branch is defined as a convolution algebra, using a vector bundle over the affine Grassmannian of G. This vector bundle over the affine Grassmannian maps to the space of loops in the representation N. We study the fibres of this maps, which live in the affine Grassmannian. We use these BFN Springer fibres to construct modules for (quantized) Coulomb branch algebras. These modules naturally correspond to boundary conditions for the corresponding gauge theory. We use our construction to partially prove a conjecture of Baumann-Kamnitzer-Knutson and give evidence for conjectures of Hikita, Nakajima, and Kamnitzer-McBreen-Proudfoot. We also prove a relation between BFN Springer fibres and quasimap spaces.
