Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904848 | Advances in Mathematics | 2018 | 70 Pages |
Abstract
While the definitions of these theories are quite different, there is a key commonality between them which makes it possible to prove that they are all isomorphic: they arise from a skew Howe dual action of glâ for some â. In this paper, we show that the construction of knot homology based on categorifying tensor products (from earlier work of the second author) fits into this framework, and thus agrees with other such homologies, such as Khovanov-Rozansky homology. We accomplish this by categorifying the action of glâÃgln on âp(CââCn) using diagrammatic bimodules. In this action, the functors corresponding to glâ and gln are quite different in nature, but they will switch roles under Koszul duality.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marco Mackaay, Ben Webster,