Simple transitive 2-representations for some 2-subcategories of Soergel bimodules
| Autor: | Volodymyr Mazorchuk, Marco Mackaay |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Fiat 2-Categories
Transitive relation Pure mathematics Algebra and Number Theory 010102 general mathematics Coxeter group Mathematics - Category Theory 01 natural sciences Equivalences Finitary 2-Categories 0103 physical sciences FOS: Mathematics Category Theory (math.CT) 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Equivalence (formal languages) Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2016.07.006 |
| Popis: | We classify simple transitive $2$-representations of certain $2$-sub\-ca\-te\-go\-ri\-es of the $2$-category of Soergel bimodules over the coinvariant algebra in Coxeter types $B_2$ and $I_2(5)$. In the $I_2(5)$ case it turns out that simple transitive $2$-representations are exhausted by cell $2$-representations. In the $B_2$ case we show that, apart from cell $2$-representations, there is a unique, up to equivalence, additional simple transitive $2$-representation and we give an explicit construction of this $2$-representation. Comment: revised version, 24 p., to appear in JPAA |
| Databáze: | OpenAIRE |
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