Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Abstract

The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive $2$-representations with a fixed apex $\mathcal{J}$ of a fiat $2$-category $\cC$ and the set of equivalence classes of faithful simple transitive $2$-representations of the fiat $2$-subquotient of $\cC$ associated with a diagonal $\mathcal{H}$-cell in $\mathcal{J}$. 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 $B_4$.

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Cited by in corpus (4)

• 2-categories of symmetric bimodules and their 2-representations
• Coidempotent subcoalgebras and short exact sequences of finitary 2-representations
• 2-representations of small quotients of Soergel bimodules in infinite types
• Adjunction in the absence of identity