On extended graphical calculus for categorified quantum $sl(n)$

Abstract

We study the properties of the extended graphical calculus for categorified quantum $sl(n)$. The main results include proofs of Reidemeister 2 and Reidemeister 3-like moves involving strands corresponding to arbitrary thicknesses and arbitrary colors -- the results that were anounced in [M. Stosic: Indecomposable objects and Lusztig's canonical basis, Math. Res. Lett. 22, no. 1 (2015), 245-278].

26 pages, plenty of TikZ pictures. We use definitions and prove some of difficult diagrammatic relations from arXiv:1105.4458. arXiv admin note: text overlap with arXiv:1105.4458