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A bimodule description of the Hecke category

Published online by Cambridge University Press:  30 September 2021

Noriyuki Abe*
Affiliation:
Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo153-8914, [email protected]

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.

Type
Research Article
Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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