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arXiv · 1812.02284

A Soergel-like category for complex reflection groups of rank one

Thomas Gobet·Anne-Laure Thiel
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Abstract

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group $W$ and a free module of rank $|W| (|W|-1)+1$ over the base ring. We also show that it is a generically semisimple algebra if defined over the complex numbers.

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Thomas Gobet, Anne-Laure Thiel. 2018-12-06. A Soergel-like category for complex reflection groups of rank one. https://arxiv.org/abs/1812.02284

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