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Abstract:

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.

Registro:

Documento: Artículo
Título:Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Autor:Rigal, L.; Zadunaisky, P.
Filiación:Université Paris 13, LAGA, UMR CNRS 7539, 99 avenue J.-B. Clément, 93430 Villetaneuse, France
Universidad de Buenos Aires, FCEN, Departamento de Matemáticas, Ciudad Universitaria, Pabellón I, (C1428EGA) - Buenos Aires, Argentina
Palabras clave:Cohen-Macaulay; Degeneration; Gorenstein; Quantum grassmannians; Quantum Richardson varieties; Quantum toric varieties; Standard monomials; Straightening laws
Año:2012
Volumen:372
Página de inicio:293
Página de fin:317
DOI: http://dx.doi.org/10.1016/j.jalgebra.2012.09.016
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v372_n_p293_Rigal.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v372_n_p293_Rigal

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Citas:

---------- APA ----------
Rigal, L. & Zadunaisky, P. (2012) . Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration. Journal of Algebra, 372, 293-317.
http://dx.doi.org/10.1016/j.jalgebra.2012.09.016
---------- CHICAGO ----------
Rigal, L., Zadunaisky, P. "Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration" . Journal of Algebra 372 (2012) : 293-317.
http://dx.doi.org/10.1016/j.jalgebra.2012.09.016
---------- MLA ----------
Rigal, L., Zadunaisky, P. "Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration" . Journal of Algebra, vol. 372, 2012, pp. 293-317.
http://dx.doi.org/10.1016/j.jalgebra.2012.09.016
---------- VANCOUVER ----------
Rigal, L., Zadunaisky, P. Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration. J. Algebra. 2012;372:293-317.
http://dx.doi.org/10.1016/j.jalgebra.2012.09.016