Abstract
We show that Khovanov homology (and its variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of –representations of categorified quantum via categorical skew Howe duality. Utilizing Cautis–Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of Jones–Wenzl projectors and their analogs purely from the higher representation theory of categorified quantum groups. In the case, this work reveals the importance of a modified class of foams introduced by Christian Blanchet which in turn suggest a similar modified version of the foam category introduced here.
Citation
Aaron D Lauda. Hoel Queffelec. David E V Rose. "Khovanov homology is a skew Howe $2$–representation of categorified quantum $\mathfrak{sl}_m$." Algebr. Geom. Topol. 15 (5) 2517 - 2608, 2015. https://doi.org/10.2140/agt.2015.15.2517
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