2018/12/06 by Thomas Gobet, Gobet, Thomas, Anne‐Laure Thiel +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1812.02284
openalex publication_date 2018/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group W and a free module of rank |W| (|W|-1)+1 over the base ring. We also show that it is a generically semisimple algebra if defined over the complex numbers.