Categorical geometric skew Howe duality

Sabin Cautis; Joel Kamnitzer; Anthony Licata

doi:10.1007/s00222-009-0227-1

Categorical geometric skew Howe duality

Sabin Cautis, Joel Kamnitzer^*, Anthony Licata

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

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(Sl₂) 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.

Original language	English
Pages (from-to)	111-159
Number of pages	49
Journal	Inventiones Mathematicae
Volume	180
Issue number	1
DOIs	https://doi.org/10.1007/s00222-009-0227-1
Publication status	Published - Feb 2010
Externally published	Yes

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Categorical geometric skew Howe duality

Abstract

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