The picture, as I understand it, is that Hecke algebras (of type A, i.e. associated to the symmetric group $S_n$) lead to the HOMFLY-PT polynomials, and the categorified version of this says that the category of Soergel bimodules (again of type A) leads to Khovanov-Rozansky homology. The main paper outlining this is "Triply-graded link homology and Hochschild homology of Soergel bimodules" (Khovanov).

However Hecke algebras, and Soergel bimodules can be defined for any Coxeter group. I'm particularly interested in type B, and the paper "Markov traces and knot invariants related to Iwahori-Hecke algebras of type B" (Geck, Lambropoulou) seems to show the connection between Hecke algebras and HOMFLY-PT polys extends to this case. Is there a categorification of this? i.e. a type B version of Khovanov-Rozansky homology? references/papers would be great if so.