Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux

Detalhes bibliográficos
Autor(a) principal: Cain, Alan J.
Data de Publicação: 2017
Outros Autores: Malheiro, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.1007/s10801-016-0714-6
Resumo: FCT fellowship (IF/01622/2013/CP1161/CT0001).
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spelling Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableauxHypoplacticQuasi-ribbon tableauRobinson-Schensted-Knuth correspondenceKashiwara operatorCrystal graphMathematics(all)FCT fellowship (IF/01622/2013/CP1161/CT0001).Crystal graphs, in the sense of Kashiwara, carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components of the crystal. In the particular case of the crystal graph for the q-analogue of the special linear Lie algebra , this monoid is the celebrated plactic monoid, whose elements can be identified with Young tableaux. The crystal graph and the so-called Kashiwara operators interact beautifully with the combinatorics of Young tableaux and with the Robinson-Schensted-Knuth correspondence and so provide powerful combinatorial tools to work with them. This paper constructs an analogous 'quasi-crystal' structure for the hypoplactic monoid, whose elements can be identified with quasi-ribbon tableaux and whose connection with the theory of quasi-symmetric functions echoes the connection of the plactic monoid with the theory of symmetric functions. This quasi-crystal structure and the associated quasi-Kashiwara operators are shown to interact just as neatly with the combinatorics of quasi-ribbon tableaux and with the hypoplactic version of the Robinson-Schensted-Knuth correspondence. A study is then made of the interaction of the crystal graph for the plactic monoid and the quasi-crystal graph for the hypoplactic monoid. Finally, the quasi-crystal structure is applied to prove some new results about the hypoplactic monoid.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNCain, Alan J.Malheiro, António2019-07-12T22:24:33Z2017-032017-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1007/s10801-016-0714-6eng0925-9899PURE: 3275289http://www.scopus.com/inward/record.url?scp=84988709956&partnerID=8YFLogxKhttps://doi.org/10.1007/s10801-016-0714-6info: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:RCAAP2024-03-11T04:34:28Zoai:run.unl.pt:10362/75282Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:35:30.317142Repositório 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 Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
title Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
spellingShingle Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
Cain, Alan J.
Hypoplactic
Quasi-ribbon tableau
Robinson-Schensted-Knuth correspondence
Kashiwara operator
Crystal graph
Mathematics(all)
title_short Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
title_full Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
title_fullStr Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
title_full_unstemmed Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
title_sort Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux
author Cain, Alan J.
author_facet Cain, Alan J.
Malheiro, António
author_role author
author2 Malheiro, António
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Cain, Alan J.
Malheiro, António
dc.subject.por.fl_str_mv Hypoplactic
Quasi-ribbon tableau
Robinson-Schensted-Knuth correspondence
Kashiwara operator
Crystal graph
Mathematics(all)
topic Hypoplactic
Quasi-ribbon tableau
Robinson-Schensted-Knuth correspondence
Kashiwara operator
Crystal graph
Mathematics(all)
description FCT fellowship (IF/01622/2013/CP1161/CT0001).
publishDate 2017
dc.date.none.fl_str_mv 2017-03
2017-03-01T00:00:00Z
2019-07-12T22:24:33Z
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 https://doi.org/10.1007/s10801-016-0714-6
url https://doi.org/10.1007/s10801-016-0714-6
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0925-9899
PURE: 3275289
http://www.scopus.com/inward/record.url?scp=84988709956&partnerID=8YFLogxK
https://doi.org/10.1007/s10801-016-0714-6
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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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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