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

2018/02/06 by Mackaay, Marco, Mazorchuk, Volodymyr, Miemietz, Vanessa +1
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1802.02078

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 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 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 B₃ and B₄.

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