Trihedral Soergel bimodules

Detalhes bibliográficos
Autor(a) principal: Mackaay, Marco
Data de Publicação: 2018
Outros Autores: Mazorchuk, Volodymyr, Miemietz, Vanessa, Tubbenhauer, Daniel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/15113
Resumo: The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl(2) representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal cate-gories, which are indexed by bicolored ADE Dynldn diagrams. Using the quantum Satake correspondence between affine A(2) Soergel bimodules and the semisimple quotient of the quantum sl(3)representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.
id RCAP_fa2042ef128821f04b7985f356b07fae
oai_identifier_str oai:sapientia.ualg.pt:10400.1/15113
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Trihedral Soergel bimodules2-representation theoryEcke algebrasSoergel bimodulesZigzag algebrasQuantum groups and their fusion categoriesThe quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl(2) representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal cate-gories, which are indexed by bicolored ADE Dynldn diagrams. Using the quantum Satake correspondence between affine A(2) Soergel bimodules and the semisimple quotient of the quantum sl(3)representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.Instytut MatematycznySapientiaMackaay, MarcoMazorchuk, VolodymyrMiemietz, VanessaTubbenhauer, Daniel2021-02-17T15:49:22Z2018-04-242018-04-24T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/15113eng0016-273610.4064/fm566-3-2019info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:27:30Zoai:sapientia.ualg.pt:10400.1/15113Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:06:00.675417Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Trihedral Soergel bimodules
title Trihedral Soergel bimodules
spellingShingle Trihedral Soergel bimodules
Mackaay, Marco
2-representation theory
Ecke algebras
Soergel bimodules
Zigzag algebras
Quantum groups and their fusion categories
title_short Trihedral Soergel bimodules
title_full Trihedral Soergel bimodules
title_fullStr Trihedral Soergel bimodules
title_full_unstemmed Trihedral Soergel bimodules
title_sort Trihedral Soergel bimodules
author Mackaay, Marco
author_facet Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
author_role author
author2 Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
author2_role author
author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Mackaay, Marco
Mazorchuk, Volodymyr
Miemietz, Vanessa
Tubbenhauer, Daniel
dc.subject.por.fl_str_mv 2-representation theory
Ecke algebras
Soergel bimodules
Zigzag algebras
Quantum groups and their fusion categories
topic 2-representation theory
Ecke algebras
Soergel bimodules
Zigzag algebras
Quantum groups and their fusion categories
description The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl(2) representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal cate-gories, which are indexed by bicolored ADE Dynldn diagrams. Using the quantum Satake correspondence between affine A(2) Soergel bimodules and the semisimple quotient of the quantum sl(3)representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.
publishDate 2018
dc.date.none.fl_str_mv 2018-04-24
2018-04-24T00:00:00Z
2021-02-17T15:49:22Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.1/15113
url http://hdl.handle.net/10400.1/15113
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0016-2736
10.4064/fm566-3-2019
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Instytut Matematyczny
publisher.none.fl_str_mv Instytut Matematyczny
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799133300720140288

Registros relacionados