Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration

Autores
Rigal, L.; Zadunaisky, P.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen-Macaulayness... in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties. © 2012 Elsevier Inc.
Fuente
J. Algebra 2012;372:293-317
Materia
Cohen-Macaulay
Degeneration
Gorenstein
Quantum grassmannians
Quantum Richardson varieties
Quantum toric varieties
Standard monomials
Straightening laws
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00218693_v372_n_p293_Rigal
Acceder
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oai_identifier_str paperaa:paper_00218693_v372_n_p293_Rigal
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Quantum analogues of Richardson varieties in the grassmannian and their toric degenerationRigal, L.Zadunaisky, P.Cohen-MacaulayDegenerationGorensteinQuantum grassmanniansQuantum Richardson varietiesQuantum toric varietiesStandard monomialsStraightening lawsIn the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen-Macaulayness... in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties. © 2012 Elsevier Inc.2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_RigalJ. Algebra 2012;372:293-317reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-23T11:18:15Zpaperaa:paper_00218693_v372_n_p293_RigalInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-23 11:18:17.146Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
spellingShingle Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Rigal, L.
Cohen-Macaulay
Degeneration
Gorenstein
Quantum grassmannians
Quantum Richardson varieties
Quantum toric varieties
Standard monomials
Straightening laws
title_short Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_full Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_fullStr Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_full_unstemmed Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
title_sort Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
dc.creator.none.fl_str_mv Rigal, L.
Zadunaisky, P.
author Rigal, L.
author_facet Rigal, L.
Zadunaisky, P.
author_role author
author2 Zadunaisky, P.
author2_role author
dc.subject.none.fl_str_mv Cohen-Macaulay
Degeneration
Gorenstein
Quantum grassmannians
Quantum Richardson varieties
Quantum toric varieties
Standard monomials
Straightening laws
topic Cohen-Macaulay
Degeneration
Gorenstein
Quantum grassmannians
Quantum Richardson varieties
Quantum toric varieties
Standard monomials
Straightening laws
dc.description.none.fl_txt_mv In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen-Macaulayness... in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties. © 2012 Elsevier Inc.
description In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate rings of Richardson varieties which appear naturally in the theory of quantum groups. Our point of view, here, is geometric: we are interested in the regularity properties of these non-commutative varieties, such as their irreducibility, normality, Cohen-Macaulayness... in the spirit of non-commutative algebraic geometry. A major step in our approach is to show that these algebras have the structure of an algebra with a straightening law. From this, it follows that they degenerate to some quantum analogues of toric varieties. © 2012 Elsevier Inc.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/20.500.12110/paper_00218693_v372_n_p293_Rigal
url http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Algebra 2012;372:293-317
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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