Simple transitive 2-representations for some 2-subcategories of Soergel bimodules

We classify simple transitive 2-representations of certain 2-subcategories of the 2-category of Soergel bimodules over the coinvariant algebra in Coxeter types B2B2 and I2(5)I2(5). In the I2(5)I2(5) case it turns out that simple transitive 2-representations are exhausted by cell 2-representations. In the B2B2 case we show that, apart from cell 2-representations, there is a unique, up to equivalence, additional simple transitive 2-representation and we give an explicit construction of this 2-representation.