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- Simple transitive 2-representations of small quotients of Soergel bimodulesPublication . Kildetoft, Tobias; Mackaay, Marco; Mazorchuk, Volodymyr; Zimmermann, JakobIn all finite Coxeter types but I-2(12), I-2(18), and I-2(30), we classify simple transitive 2-representations for the quotient of the 2-category of Soergel bimodules over the coinvariant algebra which is associated with the two-sided cell that is the closest one to the two-sided cell containing the identity element. It turns out that, in most of the cases, simple transitive 2-representations are exhausted by cell 2-representations. However, in Coxeter types I-2(2k), where k >= 3, there exist simple transitive 2-representations which are not equivalent to cell 2-representations.
- Simple transitive 2-representations via (Co-)Algebra 1-MorphismsPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, DanielFor any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.