Simple transitive 2-representations of small quotients of Soergel bimodules

Kildetoft, Tobias; Mackaay, Marco; Mazorchuk, Volodymyr; Zimmermann, Jakob

http://hdl.handle.net/10400.1/15107

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In 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.