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

JOURNAL OF ALGEBRA

卷:372

Article

Rigal, L.¹  Zadunaisky, P.² 

[1] Univ Paris 13, LAGA, UMR CNRS 7539, F-93430 Villetaneuse, France

[2] Univ Buenos Aires, FCEN, Dept Matemat, Buenos Aires, DF, Argentina

关键词: Quantum grassmannians;    Quantum Richardson varieties;    Quantum toric varieties;    Straightening laws;    Standard monomials;    Degeneration;    Cohen-Macaulay;    Gorenstein;   

DOI  :  10.1016/j.jalgebra.2012.09.016

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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