Two-color Soergel Calculus and Simple transitive 2-representations
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/15115 |
Resumo: | In this paper we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give an explicit construction of a graded (non-strict) version of all these 2-representations. Moreover, we give simple combinatorial criteria for when two such 2-representations are equivalent and for when their Grothendieck groups give rise to isomorphic representations. Finally, our construction also gives a large class of simple transitive 2-representations in infinite dihedral type for general bipartite graphs. |
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Two-color Soergel Calculus and Simple transitive 2-representations2-representation theoryZigzag algebraSoergel bimoduleHecke algebras for dihedral groupsCategorificationKazhdan-Lusztig theoryIn this paper we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give an explicit construction of a graded (non-strict) version of all these 2-representations. Moreover, we give simple combinatorial criteria for when two such 2-representations are equivalent and for when their Grothendieck groups give rise to isomorphic representations. Finally, our construction also gives a large class of simple transitive 2-representations in infinite dihedral type for general bipartite graphs.University of Toronto PressSapientiaMackaaij, MarcoTubbenhauer, Daniel2021-02-18T10:15:38Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/15115eng0008-414X10.4153/CJM-2017-061-2info: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:10400.1/15115Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:06:00.996044Repositório 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 |
Two-color Soergel Calculus and Simple transitive 2-representations |
title |
Two-color Soergel Calculus and Simple transitive 2-representations |
spellingShingle |
Two-color Soergel Calculus and Simple transitive 2-representations Mackaaij, Marco 2-representation theory Zigzag algebra Soergel bimodule Hecke algebras for dihedral groups Categorification Kazhdan-Lusztig theory |
title_short |
Two-color Soergel Calculus and Simple transitive 2-representations |
title_full |
Two-color Soergel Calculus and Simple transitive 2-representations |
title_fullStr |
Two-color Soergel Calculus and Simple transitive 2-representations |
title_full_unstemmed |
Two-color Soergel Calculus and Simple transitive 2-representations |
title_sort |
Two-color Soergel Calculus and Simple transitive 2-representations |
author |
Mackaaij, Marco |
author_facet |
Mackaaij, Marco Tubbenhauer, Daniel |
author_role |
author |
author2 |
Tubbenhauer, Daniel |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Mackaaij, Marco Tubbenhauer, Daniel |
dc.subject.por.fl_str_mv |
2-representation theory Zigzag algebra Soergel bimodule Hecke algebras for dihedral groups Categorification Kazhdan-Lusztig theory |
topic |
2-representation theory Zigzag algebra Soergel bimodule Hecke algebras for dihedral groups Categorification Kazhdan-Lusztig theory |
description |
In this paper we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of ADE type to give an explicit construction of a graded (non-strict) version of all these 2-representations. Moreover, we give simple combinatorial criteria for when two such 2-representations are equivalent and for when their Grothendieck groups give rise to isomorphic representations. Finally, our construction also gives a large class of simple transitive 2-representations in infinite dihedral type for general bipartite graphs. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019 2019-01-01T00:00:00Z 2021-02-18T10:15:38Z |
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/10400.1/15115 |
url |
http://hdl.handle.net/10400.1/15115 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0008-414X 10.4153/CJM-2017-061-2 |
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 |
University of Toronto Press |
publisher.none.fl_str_mv |
University of Toronto Press |
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 |
|
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1799133300737966080 |