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- Analogues of centralizer subalgebras for fiat 2-categories and their 2-representationsPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Zhang, XiaotingThe main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.
- Simple transitive $2$-representations of Soergel bimodules for finite Coxeter typesPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, Daniel; Zhang, XiaotingIn this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive $2$-representations and we complete their classification in all types but $H_{3}$ and $H_{4}$.
- Analogues of centralizer subalgebras for fiat 2-categories and their 2-representationsPublication . Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Zhang, XiaotingThe main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex J of a fiat 2-category C and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of C associated with a diagonal H-cell in J. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types B-3 and B-4.