Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
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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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v372_n_p293_Rigal http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal |
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paper:paper_00218693_v372_n_p293_Rigal2023-06-08T14:42:26Z Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v372_n_p293_Rigal http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 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. |
| 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 |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v372_n_p293_Rigal http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal |
| _version_ |
1768546569796190208 |