# Thomas Gobet (University of Sydney)

## On some generalizations of Soergel categories in small ranks

We describe the split Grothendieck ring of an extended category of Soergel bimodules attached to a Coxeter group of type $$A_2$$, obtained by taking one generator per reflection. This gives rise to an algebra which is a quotient of the corresponding affine Hecke algebra, and contains the (spherical) Hecke algebra of type $$A_2$$ as a subalgebra. We also sketch the construction of a category which is defined in a similar way as Soergel's one, attached to a complex reflection group of rank one. This is joint work with Anne-Laure Thiel.