On generalized categories of Soergel bimodules in type A2
Abstract
In this note, we compute the split Grothendieck ring of a generalized category of Soergel bimodules of type A2, where we take one generator for each reflection. We give a presentation by generators and relations of it and a parametrization of the indecomposable objects in the category, by realizing them as rings of regular functions on certain unions of graphs of group elements on a reflection faithful representation.
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