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Title:
Schur-Weyl duality and sutured Khovanov homology
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Abstract:
If V is a finite dimensional complex vector space, then the nth tensor power of V admits commuting actions of sl(V) and S_n, hence admits a simultaneous decomposition into irreducible representations of both. → Now let K be a framed knot in S^3 and n a positive integer. I will describe how to use a "sutured" version of Khovanov homology to associate to the pair (K,n) a graded vector space admitting commuting actions of sl(2) and S_n. When K is the 0-framed unknot, we recover classical Schur-Weyl duality for the nth tensor power of the defining representation of sl(2). This is joint work with Tony Licata and Stephan Wehrli.
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