Simple transitive 2-representations for some 2-subcategories of Soergel bimodules

Mackaay, Marco; Mazorchuk, Volodymyr

http://hdl.handle.net/10400.1/13218

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Authors

Mackaay, Marco

Mazorchuk, Volodymyr

Abstract(s)

We classify simple transitive 2-representations of certain 2-subcategories of the 2-category of Soergel bimodules over the coinvariant algebra in Coxeter types B-2 and I-2(5). In the I-2(5) case it turns out that simple transitive 2-representations are exhausted by cell 2-representations. In the B-2 case we show that, apart from cell 2-representations, there is a unique, up to equivalence, additional simple transitive 2-representation and we give an explicit construction of this 2-representation. (C) 2016 Elsevier B.V. All rights reserved.