Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients

We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if Sλ(V ) appears as a summand in the decomposition into irreducibles...

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Autores: Gutiérrez Cáceres, Álvaro, Rosas Celis, Mercedes Helena
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/154710
Acceso en línea:https://hdl.handle.net/11441/154710
https://doi.org/10.5802/crmath.468
Access Level:acceso abierto
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spelling Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficientsConditions nécessaires de positivité pour les coefficients de Littlewood–Richardson et du pléthysmeGutiérrez Cáceres, ÁlvaroRosas Celis, Mercedes HelenaWe give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if Sλ(V ) appears as a summand in the decomposition into irreducibles of Sμ(Sν(V )), then ν’s diagram is contained in λ’s diagram.Nous donnons des conditions nécessaires de positivité pour les coefficients de Littlewood– Richardson et pour les coefficients SXP. Nous en déduisons la condition nécessaire de positivité suivante pour les coefficients du pléthysme: si Sλ(V ) apparaît dans la décomposition en irréductibles de Sμ(Sν(V )), alors le diagramme de ν est contenu dans celui de λ.Académie des SciencesÁlgebraFQM333: Álgebra computacional en anillos no conmutativos y aplicaciones2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/154710https://doi.org/10.5802/crmath.468reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComptes Rendus Mathématique, 361, 1163-1173.https://doi.org/10.5802/crmath.468info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1547102026-06-17T12:51:07Z
dc.title.none.fl_str_mv Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
Conditions nécessaires de positivité pour les coefficients de Littlewood–Richardson et du pléthysme
title Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
spellingShingle Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
Gutiérrez Cáceres, Álvaro
title_short Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
title_full Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
title_fullStr Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
title_full_unstemmed Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
title_sort Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients
dc.creator.none.fl_str_mv Gutiérrez Cáceres, Álvaro
Rosas Celis, Mercedes Helena
author Gutiérrez Cáceres, Álvaro
author_facet Gutiérrez Cáceres, Álvaro
Rosas Celis, Mercedes Helena
author_role author
author2 Rosas Celis, Mercedes Helena
author2_role author
dc.contributor.none.fl_str_mv Álgebra
FQM333: Álgebra computacional en anillos no conmutativos y aplicaciones
description We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if Sλ(V ) appears as a summand in the decomposition into irreducibles of Sμ(Sν(V )), then ν’s diagram is contained in λ’s diagram.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/154710
https://doi.org/10.5802/crmath.468
url https://hdl.handle.net/11441/154710
https://doi.org/10.5802/crmath.468
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Comptes Rendus Mathématique, 361, 1163-1173.
https://doi.org/10.5802/crmath.468
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Académie des Sciences
publisher.none.fl_str_mv Académie des Sciences
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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