Symmetric Khovanov--Rozansky link homologies

Thursday, 5 September, 2019

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We provide a finite dimensional categorification of the symmetric evaluation of \mathfrak{sl}_N-webs using foam technology. As an output we obtain a symmetric link homology theory categorifying the link invariant associated to symmetric powers of the standard representation of \mathfrak{sl}_N. In addition, the construction is actually made in an equivariant setting. We prove also that there is a spectral sequence from the Khovanov-Rozansky triply graded link homology to the symmetric one and provide along the way a foam interpretation of Soergel bimodules.


Louis-Hadrien Robert
Emmanuel Wagner