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...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_00218693_v372_n_p293_Rigal |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v372_n_p293_Rigal |
| Access Level: | acceso abierto |
| Palabra clave: | Cohen-Macaulay Degeneration Gorenstein Quantum grassmannians Quantum Richardson varieties Quantum toric varieties Standard monomials Straightening laws |
| Sumario: | 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. |
|---|