Abstract
In this paper, which is a follow-up to [38], I define and study slN-web algebras, for any N⩾2. For N=2 these algebras are isomorphic to Khovanov's [22] arc algebras and for N=3 they are Morita equivalent to the sl3-web algebras which I defined and studied together with Pan and Tubbenhauer [34].The main result of this paper is that the slN-web algebras are Morita equivalent to blocks of certain level-N cyclotomic KLR algebras, for which I use the categorified quantum skew Howe duality defined in [38].Using this Morita equivalence and Brundan and Kleshchev's [4] work on cyclotomic KLR-algebras, I show that there exists an isomorphism between a certain space of slN-webs and the split Grothendieck group of the corresponding slN-web algebra, which maps the dual canonical basis elements to the Grothendieck classes of the indecomposable projective modules (with a certain normalization of their grading).
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