Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10400.1/15105 |
Resumo: | We associate a monoidal category H-lambda to each dominant integral weight lambda of sl(p) or sl(infinity). These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to lambda. We show that, in the sl infinity case, the level d Heisenberg algebra embeds into the Grothendieck ring of H-lambda, where d is the level of lambda. The categories H-lambda can be viewed as a graphical calculus describing induction and restriction functors between categories of modules for degenerate cyclotomic Hecke algebras, together with their natural transformations. As an application of this tool, we prove a new result concerning centralizers for degenerate cyclotomic Hecke algebras. |
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Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorificationCategorificationHeisenberg algebraHecke algebrasCyclotomic quotientsDiagrammatic calculusWe associate a monoidal category H-lambda to each dominant integral weight lambda of sl(p) or sl(infinity). These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to lambda. We show that, in the sl infinity case, the level d Heisenberg algebra embeds into the Grothendieck ring of H-lambda, where d is the level of lambda. The categories H-lambda can be viewed as a graphical calculus describing induction and restriction functors between categories of modules for degenerate cyclotomic Hecke algebras, together with their natural transformations. As an application of this tool, we prove a new result concerning centralizers for degenerate cyclotomic Hecke algebras.Academic PressSapientiaMackaay, MarcoSavage, Alistair2021-02-16T16:01:11Z2017-05-082017-05-08T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/15105eng0021-869310.1016/j.jalgebra.2018.03.004info: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:10400.1/15105Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:06:00.404600Repositório 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 |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
title |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
spellingShingle |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification Mackaay, Marco Categorification Heisenberg algebra Hecke algebras Cyclotomic quotients Diagrammatic calculus |
title_short |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
title_full |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
title_fullStr |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
title_full_unstemmed |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
title_sort |
Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification |
author |
Mackaay, Marco |
author_facet |
Mackaay, Marco Savage, Alistair |
author_role |
author |
author2 |
Savage, Alistair |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Mackaay, Marco Savage, Alistair |
dc.subject.por.fl_str_mv |
Categorification Heisenberg algebra Hecke algebras Cyclotomic quotients Diagrammatic calculus |
topic |
Categorification Heisenberg algebra Hecke algebras Cyclotomic quotients Diagrammatic calculus |
description |
We associate a monoidal category H-lambda to each dominant integral weight lambda of sl(p) or sl(infinity). These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to lambda. We show that, in the sl infinity case, the level d Heisenberg algebra embeds into the Grothendieck ring of H-lambda, where d is the level of lambda. The categories H-lambda can be viewed as a graphical calculus describing induction and restriction functors between categories of modules for degenerate cyclotomic Hecke algebras, together with their natural transformations. As an application of this tool, we prove a new result concerning centralizers for degenerate cyclotomic Hecke algebras. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-05-08 2017-05-08T00:00:00Z 2021-02-16T16:01:11Z |
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/10400.1/15105 |
url |
http://hdl.handle.net/10400.1/15105 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0021-8693 10.1016/j.jalgebra.2018.03.004 |
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 |
Academic Press |
publisher.none.fl_str_mv |
Academic 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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1799133300708605952 |