1 results
ANALOGUES OF CENTRALIZER SUBALGEBRAS FOR FIAT 2-CATEGORIES AND THEIR 2-REPRESENTATIONS
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 6 / November 2020
- Published online by Cambridge University Press:
- 04 December 2018, pp. 1793-1829
- Print publication:
- November 2020
-
- Article
- Export citation
-
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 
$B_{4}$.
