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Matt Hogancamp, USC – Geometric Methods in Representation Theory Seminar
March 29, 2019 @ 4:00 pm - 5:00 pm
Title: Serre duality for Khovanov-Rozansky homology
Abstract: I will discuss recent joint work with Gorsky, Mellit, and Nagane in which we consider a monoidal version of Serre duality for the category of Soergel bimodules in type A, in which the role of the Serre functor is played by the Rouquier complex associated to the full twist braid. This is a lift of (the type A special case of) a result of Mazorchuk-Stroppel (2008) and Beilinson-Bezrukavnikov-Mirkovic (2004), which states that the action of the full twist is the Serre functor on the BGG category O, and as a result we obtain a new “topological” proof of this fact. I will conclude by discussing consequences for Khovanov-Rozansky link homology.