The Beilinson-Drinfeld Grassmannian and symplectic knot homology
The Beilinson-Drinfeld Grassmannian and symplectic knot homology
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Beilinson-Drinfeld Grassmannian 和辛结同源性
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发表时间：
2008
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通讯作者：
J. Kamnitzer
中科院分区：
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作者：
J. Kamnitzer
Seidel-Smith和Manolescu利用辛纤维化构造了纽结同调理论，其全空间是矩阵的某些变种。这些纽结同调理论与SL（n）和标准和对偶表示的张量积有关。在本文中，我们把他们的几何设置在一个自然的，一般的框架。对于任意复约化群和任意极小占优权序列，我们构造了一个构形空间上仿射簇的纤维化。这些变种的中上同调同构于表示的相应张量积中的不变量空间。我们的构造使用Beilinson-Drinfeld Grassmannian和几何Satake对应。
Seidel-Smith and Manolescu constructed knot homology theories using symplectic fibrations whose total spaces were certain varieties of matrices. These knot homology theories were associated to $SL(n) $ and tensor products of the standard and dual representations. In this paper, we place their geometric setups in a natural, general framework. For any complex reductive group and any sequence of minuscule dominant weights, we construct a fibration of affine varieties over a configuration space. The middle cohomology of these varieties is isomorphic to the space of invariants in the corresponding tensor product of representations. Our construction uses the Beilinson-Drinfeld Grassmannian and the geometric Satake correspondence.