# Two-color Soergel Calculus and Simple Transitive 2-representations

@article{Mackaaij2019TwocolorSC, title={Two-color Soergel Calculus and Simple Transitive 2-representations}, author={Marco Mackaaij and Daniel Tubbenhauer}, journal={Canadian Journal of Mathematics}, year={2019}, volume={71}, pages={1523 - 1566} }

Abstract In this paper, we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give an explicit construction of a graded (non-strict) version of all these 2-representations. Moreover, we give simple combinatorial criteria for when two such 2-representations are equivalent and for when their Grothendieck groups give… Expand

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