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

2017-03Artigo científico Acesso aberto
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dc.contributor.authorCain, Alan J.
dc.contributor.authorMalheiro, António
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblSpringer Verlag
dc.date.accessioned2019-07-12T22:24:33Z
dc.date.available2019-07-12T22:24:33Z
dc.date.issued2017-03
dc.descriptionFCT fellowship (IF/01622/2013/CP1161/CT0001).
dc.description.abstractCrystal 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.en
dc.description.versionauthorsversion
dc.description.versionpublished
dc.format.extent619032
dc.identifier.doi10.1007/s10801-016-0714-6
dc.identifier.issn0925-9899
dc.identifier.otherPURE: 3275289
dc.identifier.otherPURE UUID: 81d4dff0-0b18-4d6c-9622-38bb5a30d148
dc.identifier.otherWOS: 000394149700006
dc.identifier.otherScopus: 84988709956
dc.identifier.otherORCID: /0000-0003-1186-6216/work/50749045
dc.identifier.urihttp://www.scopus.com/inward/record.url?scp=84988709956&partnerID=8YFLogxK
dc.identifier.urlhttps://www.scopus.com/pages/publications/84988709956
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/5876/147204/PT
dc.subjectHypoplactic
dc.subjectQuasi-ribbon tableau
dc.subjectRobinson-Schensted-Knuth correspondence
dc.subjectKashiwara operator
dc.subjectCrystal graph
dc.subjectGeneral Mathematics
dc.titleCrystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableauxen
dc.typejournal article
degois.publication.firstPage475
degois.publication.issue2
degois.publication.lastPage524
degois.publication.titleJournal of Algebraic Combinatorics
degois.publication.volume45
dspace.entity.typePublication
oaire.awardNumberUID/MAT/00297/2013
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F00297%2F2013/PT
oaire.fundingStream5876
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublicationd9bab5fb-9f7c-4479-b4fd-4caf5303847c
relation.isProjectOfPublication.latestForDiscoveryd9bab5fb-9f7c-4479-b4fd-4caf5303847c

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