Year: 2017
Type: article
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 rise to isomorphic representations. Finally, our construction also gives a large class of simple transitive 2-representations in infinite dihedral type for general bipartite graphs.
Source: Canadian Journal of Mathematics
Authors: Marco Mackaaij, Daniel Tubbenhauer
Institutions: Instituto Superior Técnico, University of Zurich
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Hausdorff Center for Mathematics
OpenAlex ID: W2518274522