sl(N)-Web categories

Abstract

In this paper we use colored sl(N)-matrix factorizations, due to Wu and Y.Y., in order to categorify part of the quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison. In particular, we define web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We show that each such web category is equivalent to the category of finite dimensional graded projective modules over a certain level N cyclotomic Khovanov-Lauda-Rouquier algebra.

39 pages, only small changes

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• Current algebras and categorified quantum groups
• Categorified skew Howe duality and comparison of knot homologies
• Cyclicity for categorified quantum groups
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• The sl(N)-web algebras and dual canonical bases
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• A $p$-DG deformed Webster algebra of type $A_1$