info:eu-repo/semantics/article
Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Fecha
2012-12Registro en:
Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration; Elsevier Inc; Journal Of Algebra; 372; 12-2012; 293-317
0021-8693
CONICET Digital
CONICET
Autor
Rigal, L.
Zadunaisky Bustillos, Pablo Mauricio
Resumen
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.