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A bimodule description of the Hecke category
Published online by Cambridge University Press: 30 September 2021
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 when
$V$ is not reflection faithful and 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 fewer assumptions on
$V$. In this paper, we give a bimodule description of the Elias–Williamson category and re-prove the categorification theorem.
Keywords
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- Research Article
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- © 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
References
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