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- W2018733254 abstract "This paper contains a categorification of the ${frak sl}(k)$ link invariantusing parabolic singular blocks of category ${cal{O}}$. Our approach isintended to be as elementary as possible, providing essentiallycombinatorial arguments for the main results of Sussan. The justificationthat our combinatorial arguments and steps are correct usesnon-combinatorial geometric and representation theoretic results (e.g., theKazhdan-Lusztig and Soergel's theorems). We take these results as grantedand use them like axioms (called {it Facts/} in the text). We first construct an exact functor valued invariant of webs or ``special''trivalent graphs labelled with $1, 2, k-1, k$ satisfying the MOY relations.Afterwards we extend it to the ${frak sl}(k)$-invariant of links bypassing to the derived categories. The approach of Khovanov using foamsappears naturally in this context. More generally, we expect that ourapproach provides a representation theoretic interpretation of the ${fraksl}(k)$-homology, based on foams and the Kapustin-Li formula, from Mackaay,Stosic, and Vaz. Conjecturally this implies that the Khovanov-Rozansky linkhomology is obtained from our invariant by restriction." @default.
- W2018733254 created "2016-06-24" @default.
- W2018733254 creator A5007688099 @default.
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- W2018733254 date "2009-01-01" @default.
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- W2018733254 title "A combinatorial approach to functorial quantum sl<sub xmlns:m=http://www.w3.org/1998/Math/MathML xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><i>k</i></sub> knot invariants" @default.
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- W2018733254 doi "https://doi.org/10.1353/ajm.0.0082" @default.
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