Geodesic
QUANTUM ANALOGUES OF SCHUBERT VARIETIES IN THE GRASSMANNIAN
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 55-70

Voir la notice de l'article provenant de la source Cambridge University Press

We study quantum Schubert varieties from the point of view of regularity conditions. More precisely, we show that these rings are domains that 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.
DOI : 10.1017/S0017089507003928
Mots-clés : 16W35, 16P40, 16S38, 17B37, 20G42 
LENAGAN, T.H.; RIGAL, L. QUANTUM ANALOGUES OF SCHUBERT VARIETIES IN THE GRASSMANNIAN. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 55-70. doi: 10.1017/S0017089507003928
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