Quantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum grassmannians

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dc.creatorLenagan, T H
dc.creatorRigal, L
dc.date2004-03-01
dc.date.accessioned2026-07-07T05:05:49Z
dc.date.available2026-07-07T05:05:49Z
dc.descriptionWe study quantum analogues of quotient varieties, namely quantum grassmannians and quantum determinantal rings, from the point of view of regularity conditions. More precisely, we show that these rings are AS-Cohen-Macaulay and determine which of them are AS-Gorenstein. Our method is inspired by the one developed by De Concini, Eisenbud and Procesi in the commutative case. Thus, we introduce and study the notion of a quantum graded algebra with a staightening law on a partially ordered set, showing in particular that, among such algebras, those whose underlying poset is wonderful are AS-Cohen-Macaulay. Then, we prove that both quantum grassmannians and quantum determinantal rings are quantum graded algebras with a staightening law on a wonderful poset, hence showing that they are AS-Cohen-Macaulay. In this last step, we are lead to introduce and study (to some extent) natural quantum analogues of Schubert varieties.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0403021
dc.identifierhttp://arxiv.org/abs/math/0403021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70313
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject16W35; 17B37; 20G42
dc.titleQuantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum grassmannians
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