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

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DOI

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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     title = {QUANTUM {ANALOGUES} {OF} {SCHUBERT} {VARIETIES} {IN} {THE} {GRASSMANNIAN}},
     journal = {Glasgow mathematical journal},
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     year = {2008},
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