Simple transitive 2-representations of small quotients of Soergel bimodules

Kildetoft, Tobias; Mackaay, Marco; Mazorchuk, Volodymyr; Zimmermann, Jakob

doi:10.1090/tran/7456

Simple transitive $2$-representations of small quotients of Soergel bimodules
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by Tobias Kildetoft, Marco Mackaay, Volodymyr Mazorchuk and Jakob Zimmermann PDF

Trans. Amer. Math. Soc. 371 (2019), 5551-5590 Request permission

Abstract:

In all finite Coxeter types but $I_2(12)$, $I_2(18)$, and $I_2(30)$, we classify simple transitive $2$-representations for the quotient of the $2$-category of Soergel bimodules over the coinvariant algebra which is associated with the two-sided cell that is the closest one to the two-sided cell containing the identity element. It turns out that, in most of the cases, simple transitive $2$-representations are exhausted by cell $2$-representations. However, in Coxeter types $I_2(2k)$, where $k\geq 3$, there exist simple transitive $2$-representations which are not equivalent to cell $2$-representations.

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