Categorical geometric skew Howe duality
Categorical geometric skew Howe duality
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DOI：
10.1007/s00222-009-0227-1
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发表时间：
2009-02
影响因子：
3.1
通讯作者：
Sabin Cautis;J. Kamnitzer;Anthony M. Licata
中科院分区：
文献类型：
--
作者：
Sabin Cautis;J. Kamnitzer;Anthony M. Licata
通过构造仿射格拉斯曼算子中相应卷积积上相干层的导出范畴之间的等价性，我们对的极小表示的张量积之间的R-矩阵同构进行了分类.在建设的主要步骤是一个分类的表示，其中相关的表示的量子斜豪对偶。由此产生的等价性是由前两位作者开发的Reshitikhin-Turaev缠结不变量的代数几何分类程序的一部分。
We categorify the R-matrix isomorphism between tensor products of minuscule representations ofby constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations ofwhich are related to representations ofby quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometric categorification of Reshitikhin-Turaev tangle invariants developed by the first two authors.