2-representations of small quotients of Soergel bimodules in infinite types

Abstract

We determine for which Coxeter types the associated small quotient of the 2 2 -category of Soergel bimodules is finitary and, for such a small quotient, classify the simple transitive 2 2 -representations (sometimes under the additional assumption of gradability). We also describe the underlying categories of the simple transitive 2 2 -representations. For the small quotients of general Coxeter types, we give a description for the cell 2 2 -representations.