sl(N)-web categories and categorified skew Howe duality

Mackaay, Marco; Yonezawa, Yasuyoshi

http://hdl.handle.net/10400.1/14364

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Authors

Mackaay, Marco

Yonezawa, Yasuyoshi

Abstract(s)

In this paper we show how the colored Khovanov-Rozansky Sl(N)-matrix factorizations, due to Wu [45] and Y.Y. [46,47], can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define Sl(N)-web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. (C) 2018 Elsevier B.V. All rights reserved.