2019/01/08 by Noriyuki Abe, Abe, Noriyuki
Computer Science · Mathematics · #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1901.02336
openalex publication_date 2019/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.