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

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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 quan...

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Autores principales:	Rigal, L., Zadunaisky, P.
Formato:	Artículo publishedVersion
Publicado:	2012
Materias:	Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00218693_v372_n_p293_Rigal_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_00218693_v372_n_p293_Rigal_oai
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spelling	I28-R145-paper_00218693_v372_n_p293_Rigal_oai2024-08-16 Rigal, L. Zadunaisky, P. 2012 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Algebra 2012;372:293-317 Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00218693_v372_n_p293_Rigal_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws
spellingShingle	Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws Rigal, L. Zadunaisky, P. Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
topic_facet	Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws
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.
format	Artículo Artículo publishedVersion
author	Rigal, L. Zadunaisky, P.
author_facet	Rigal, L. Zadunaisky, P.
author_sort	Rigal, L.
title	Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
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
publishDate	2012
url	http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00218693_v372_n_p293_Rigal_oai
work_keys_str_mv	AT rigall quantumanaloguesofrichardsonvarietiesinthegrassmannianandtheirtoricdegeneration AT zadunaiskyp quantumanaloguesofrichardsonvarietiesinthegrassmannianandtheirtoricdegeneration
_version_	1809356777597173760

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

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