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arXiv · 1711.08814

On generalized categories of Soergel bimodules in type $A_2$

Thomas Gobet·Anne-Laure Thiel
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Abstract

In this note, we compute the split Grothendieck ring of a generalized category of Soergel bimodules of type $A_2$, 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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Thomas Gobet, Anne-Laure Thiel. 2017-11-23. On generalized categories of Soergel bimodules in type $A_2$. https://arxiv.org/abs/1711.08814

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