TheslN-web algebras and dual canonical bases

Mackaay, Marco

http://hdl.handle.net/10400.1/15095

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Authors

Mackaay, Marco

Abstract(s)

In this paper, which is a follow-up to [38], I define and study SIN-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 sl(3)-web algebras which I defined and studied together with Pan and Tubbenhauer [34]. The main result of this paper is that the SIN-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 SIN-webs and the split Grothendieck group of the corresponding SIN-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).