sl(N)-web categories and categorified skew Howe duality

Detalhes bibliográficos
Autor(a) principal: Mackaay, Marco
Data de Publicação: 2019
Outros Autores: Yonezawa, Yasuyoshi
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/14364
Resumo: In this paper we show how the colored Khovanov-Rozansky Sl(N)-matrix factorizations, due to Wu [45] and Y.Y. [46,47], can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define Sl(N)-web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. (C) 2018 Elsevier B.V. All rights reserved.
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spelling sl(N)-web categories and categorified skew Howe dualityHighest weight categoriesKnot homologyCoherent sheavesIn this paper we show how the colored Khovanov-Rozansky Sl(N)-matrix factorizations, due to Wu [45] and Y.Y. [46,47], can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define Sl(N)-web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. (C) 2018 Elsevier B.V. All rights reserved.FCT - Fundacao para a Ciencia e a TecnologiaPortuguese Foundation for Science and Technology [PTDC/MAT/101503/2008]New Geometry and TopologyElsevier Science BvSapientiaMackaay, MarcoYonezawa, Yasuyoshi2020-07-24T10:52:28Z2019-052019-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/14364eng0022-404910.1016/j.jpaa.2018.07.013info: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:RCAAP2023-07-24T10:26:39Zoai:sapientia.ualg.pt:10400.1/14364Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:05:22.832856Repositório 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 sl(N)-web categories and categorified skew Howe duality
title sl(N)-web categories and categorified skew Howe duality
spellingShingle sl(N)-web categories and categorified skew Howe duality
Mackaay, Marco
Highest weight categories
Knot homology
Coherent sheaves
title_short sl(N)-web categories and categorified skew Howe duality
title_full sl(N)-web categories and categorified skew Howe duality
title_fullStr sl(N)-web categories and categorified skew Howe duality
title_full_unstemmed sl(N)-web categories and categorified skew Howe duality
title_sort sl(N)-web categories and categorified skew Howe duality
author Mackaay, Marco
author_facet Mackaay, Marco
Yonezawa, Yasuyoshi
author_role author
author2 Yonezawa, Yasuyoshi
author2_role author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Mackaay, Marco
Yonezawa, Yasuyoshi
dc.subject.por.fl_str_mv Highest weight categories
Knot homology
Coherent sheaves
topic Highest weight categories
Knot homology
Coherent sheaves
description In this paper we show how the colored Khovanov-Rozansky Sl(N)-matrix factorizations, due to Wu [45] and Y.Y. [46,47], can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define Sl(N)-web categories and 2-representations of Khovanov and Lauda's categorical quantum sl(m) on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. (C) 2018 Elsevier B.V. All rights reserved.
publishDate 2019
dc.date.none.fl_str_mv 2019-05
2019-05-01T00:00:00Z
2020-07-24T10:52:28Z
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/10400.1/14364
url http://hdl.handle.net/10400.1/14364
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-4049
10.1016/j.jpaa.2018.07.013
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 Elsevier Science Bv
publisher.none.fl_str_mv Elsevier Science Bv
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
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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
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