Abstract
In this paper we define an explicit basis for the gln-web algebra Hn(k⃗ ) (the gln generalization of Khovanov's arc algebra) using categorified q-skew Howe duality.
Our construction is a gln-web version of Hu--Mathas' graded cellular basis and has two major applications: it gives rise to an explicit isomorphism between a certain idempotent truncation of a thick calculus cyclotomic KLR algebra and Hn(k⃗ ), and it gives an explicit graded cellular basis of the 2-hom space between two gln-webs. We use this to give a (in principle) computable version of colored Khovanov-Rozansky gln-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only F.
Tubbenhauer, Daniel