Categorical geometric skew Howe duality
arXiv:0902.1795 · doi:10.1007/s00222-009-0227-1
Abstract
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.
31 pages