Quantum analogues of Schubert varieties in the grassmannian

Details Quantum analogues of Schubert varieties in the grassmannian Quantum analogues of Schubert varieties in the grassmannian

2006-10-26

arxiv.org/abs/math/0610794v1

Mathematics

Quantum Algebra

16 pages

Scientific paper

We study quantum Schubert varieties from the point of view of regularity conditions. More precisely, we show that these rings are domains which are maximal orders and are AS-Cohen-Macaulay and we determine which of them are AS-Gorenstein. One key fact that enables us to prove these results is that quantum Schubert varieties are quantum graded algebras with a straightening law that have a unique minimal element in the defining poset. We prove a general result showing when such quantum graded algebras are maximal orders. Finally, we exploit these results to show that quantum determinantal rings are maximal orders.

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