A bimodule description of the Hecke category. (30th October 2021)

• Record Type: Journal Article
• Authors: Abe, Noriyuki
• Is Part Of: Compositio mathematica. Volume 157:Number 10(2021)
• Page Start: 2133
• Page End: 2159
• Publication Date: 2021-10-30
• Subjects: Hecke algebra -- Soergel bimodules; 20F55 -- 20G05; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X21007466
• Languages: English
• ISSNs: 0010-437X

Abstract

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.