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arXiv · 1901.02336

On Soergel bimodules

Noriyuki Abe
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Abstract

For a Coxeter system and a representation $V$ of this Coxeter system, Soergel defined a category which is now called the category of Soergel bimodules and proved that this gives a categorification of the Hecke algebra when $V$ is reflection faithful. Elias and Williamson defined another category even when $V$ is not reflection faithful and they proved that this category is equivalent to the category of Soergel bimodules when $V$ is reflection faithful. Moreover they proved the categorification theorem for their category with less assumptions on $V$. In this paper, we give a "bimodule theoretic" definition of the category of Elias-Williamson and reprove the categorification theorem.

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Noriyuki Abe. 2020-09-22. On Soergel bimodules. https://arxiv.org/abs/1901.02336

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