Algebras with straightening law on posets of minors

1988 ◽  
pp. 38-49
Author(s):  
Winfried Bruns ◽  
Udo Vetter
Keyword(s):  
Straightening Law

scholarly journals QUANTUM ANALOGUES OF SCHUBERT VARIETIES IN THE GRASSMANNIAN

2008 ◽  
Vol 50 (1) ◽  
pp. 55-70 ◽  
Author(s):  
T.H. LENAGAN ◽  
L. RIGAL
Keyword(s):  
General Result ◽  
Minimal Element ◽  
Point Of View ◽  
Schubert Varieties ◽  
Regularity Conditions ◽  
Graded Algebras ◽  
Maximal Orders ◽  
Straightening Law

AbstractWe 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.

scholarly journals Rings with lexicographic straightening law

1981 ◽  
Vol 39 (2) ◽  
pp. 185-213 ◽  
Author(s):  
Kenneth Baclawski
Keyword(s):  
Straightening Law
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