Simple transitive 2-representations of small quotients of Soergel\n bimodules

2016/05/04 by Tobias Kildetoft, Marco Mackaay, Kildetoft, Tobias +5 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Artin group #Combinatorics #Coxeter complex #Coxeter element #Coxeter group #Longest element of a Coxeter group #Mathematics #Pure mathematics #Quotient #Simple (philosophy) #Transitive relation #math.CT #math.RT

paper · pdf · doi:10.48550/arxiv.1605.01373

Revised version to appear in Trans. AMS

openalex publication_date 2016/05/04 · arxiv created 2017/11/09 · arxiv updated 2017/11/10 · openalex created_date 2022/09/28 · openalex updated_date 2026/08/05

Abstract

In all finite Coxeter types but I₂(12), I₂(18) and I₂(30), we\nclassify simple transitive 2-rep -re -sen -ta -ti -ons for the quotient of\nthe 2-category of Soergel bimodules over the coinvariant algebra which is\nassociated to the two-sided cell that is the closest one to the two-sided cell\ncontaining the identity element. It turns out that, in most of the cases,\nsimple transitive 2-representations are exhausted by cell\n2-representations. However, in Coxeter types I₂(2k), where k\≥ 3,\nthere exist simple transitive 2-representations which are not equivalent to\ncell 2-representations.\n

Cited by

• Combinatorics of monoidal actions in Lie-algebraic context
• Infinite rank module categories over finite dimensional sl 2 \mathfrak sl₂ German sl 2-modules in Lie algebraic-context

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