Categorical Geometric Skew Howe Duality
نویسندگان
چکیده
We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) 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 Uq(sl2) which are related to representations of Uq(sln) 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.
منابع مشابه
Geometric Symmetric
We provide a natural geometric setting for symmetric Howe duality. This is realized as a (loop) sln action on derived categories of coherent sheaves on certain varieties arising in the geometry of the Beilinson-Drinfeld Grassmannian. The main construction parallels our earlier work on categorical sln actions and skew Howe duality. In that case the varieties involved arose in the geometry of the...
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We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) 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 Uq(sl2) which are related to representations of Uq(sln) by quant...
متن کاملar X iv : 0 90 2 . 17 95 v 2 [ m at h . A G ] 1 9 N ov 2 00 9 CATEGORICAL GEOMETRIC SKEW HOWE DUALITY
We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) 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 Uq(sl2) which are related to representations of Uq(sln) by quant...
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