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arXiv · 0902.1795

Categorical geometric skew Howe duality

Sabin Cautis·Joel Kamnitzer·Anthony Licata
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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.

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Sabin Cautis, Joel Kamnitzer, Anthony Licata. 2009-11-19. Categorical geometric skew Howe duality. https://doi.org/10.1007/s00222-009-0227-1

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