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

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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 of a fiat 2-category and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of associated with a diagonal-cell in. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types and.

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Original languageEnglish
Pages (from-to)1793-1829
Number of pages37
JournalJournal of the Institute of Mathematics of Jussieu
Volume19
Issue number6
Early online date4 Dec 2018
DOIs
Publication statusPublished - Nov 2020
Peer-reviewedYes

Keywords

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  • 2-category, Green relations, coalgebra 1-morphism, cotensor product, simple transitive 2-representation

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