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ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT 2-CATEGORIES AND THEIR 2-REPRESENTATIONS
Published online by Cambridge University Press: 04 December 2018
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
$\mathscr{C}$ and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of
$\mathscr{C}$ 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
$B_{4}$.
Keywords
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 6 , November 2020 , pp. 1793 - 1829
- Copyright
- © Cambridge University Press 2018
References
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