Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules

Autores
Futorny, Vyacheslav; Grantcharov, Dimitar; Ramirez, Luis Enrique; Zadunaisky Bustillos, Pablo Mauricio
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module appears as the socle of a universal tableaux module. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. We also give a very explicit description of the support and essential support of the simple singular Verma module M(−ρ).
Fil: Futorny, Vyacheslav. Universidade de Sao Paulo; Brasil
Fil: Grantcharov, Dimitar. University of Texas; Estados Unidos
Fil: Ramirez, Luis Enrique. Universidad Federal Do Abc; Brasil
Fil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
GELFAND-TSETLIN BASES
GELFAND-TSETLIN MODULES
REFLECTION GROUPS
VERMA MODULES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/139098
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modulesFutorny, VyacheslavGrantcharov, DimitarRamirez, Luis EnriqueZadunaisky Bustillos, Pablo MauricioGELFAND-TSETLIN BASESGELFAND-TSETLIN MODULESREFLECTION GROUPSVERMA MODULEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module appears as the socle of a universal tableaux module. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. We also give a very explicit description of the support and essential support of the simple singular Verma module M(−ρ).Fil: Futorny, Vyacheslav. Universidade de Sao Paulo; BrasilFil: Grantcharov, Dimitar. University of Texas; Estados UnidosFil: Ramirez, Luis Enrique. Universidad Federal Do Abc; BrasilFil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2020-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/139098Futorny, Vyacheslav; Grantcharov, Dimitar; Ramirez, Luis Enrique; Zadunaisky Bustillos, Pablo Mauricio; Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules; Academic Press Inc Elsevier Science; Journal of Algebra; 556; 8-2020; 412-4360021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869320301289?via%3Dihubinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2020.02.032info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1811.07992info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:50Zoai:ri.conicet.gov.ar:11336/139098instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:36:50.537CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
title Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
spellingShingle Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
Futorny, Vyacheslav
GELFAND-TSETLIN BASES
GELFAND-TSETLIN MODULES
REFLECTION GROUPS
VERMA MODULES
title_short Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
title_full Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
title_fullStr Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
title_full_unstemmed Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
title_sort Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
dc.creator.none.fl_str_mv Futorny, Vyacheslav
Grantcharov, Dimitar
Ramirez, Luis Enrique
Zadunaisky Bustillos, Pablo Mauricio
author Futorny, Vyacheslav
author_facet Futorny, Vyacheslav
Grantcharov, Dimitar
Ramirez, Luis Enrique
Zadunaisky Bustillos, Pablo Mauricio
author_role author
author2 Grantcharov, Dimitar
Ramirez, Luis Enrique
Zadunaisky Bustillos, Pablo Mauricio
author2_role author
author
author
dc.subject.none.fl_str_mv GELFAND-TSETLIN BASES
GELFAND-TSETLIN MODULES
REFLECTION GROUPS
VERMA MODULES
topic GELFAND-TSETLIN BASES
GELFAND-TSETLIN MODULES
REFLECTION GROUPS
VERMA MODULES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module appears as the socle of a universal tableaux module. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. We also give a very explicit description of the support and essential support of the simple singular Verma module M(−ρ).
Fil: Futorny, Vyacheslav. Universidade de Sao Paulo; Brasil
Fil: Grantcharov, Dimitar. University of Texas; Estados Unidos
Fil: Ramirez, Luis Enrique. Universidad Federal Do Abc; Brasil
Fil: Zadunaisky Bustillos, Pablo Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module appears as the socle of a universal tableaux module. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. We also give a very explicit description of the support and essential support of the simple singular Verma module M(−ρ).
publishDate 2020
dc.date.none.fl_str_mv 2020-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/139098
Futorny, Vyacheslav; Grantcharov, Dimitar; Ramirez, Luis Enrique; Zadunaisky Bustillos, Pablo Mauricio; Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules; Academic Press Inc Elsevier Science; Journal of Algebra; 556; 8-2020; 412-436
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/139098
identifier_str_mv Futorny, Vyacheslav; Grantcharov, Dimitar; Ramirez, Luis Enrique; Zadunaisky Bustillos, Pablo Mauricio; Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules; Academic Press Inc Elsevier Science; Journal of Algebra; 556; 8-2020; 412-436
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021869320301289?via%3Dihub
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2020.02.032
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1811.07992
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613157388025856
score 13.070432

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