Categorical geometric skew Howe duality

• 成果类型: Article
• 署名作者: Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony
• 署名单位: University of Toronto; Stanford University; Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0227-1
• 发表日期: 2010
• 页码: 111-159
• 关键词: multiplicative formula; coherent sheaves; knot homology; weyl group

摘要

We categorify the R-matrix isomorphism between tensor products of minuscule representations of U-q (sl(n)) by 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 of U-q (sl(2)) which are related to representations of U-q (sl(n)) by 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.