We show that the classification of $A$-hypergeometric systems and that of multi-graded simple modules (up to shift) over the ring of differential operators on an affine toric variety are the same. We then show that the set of multi-homogeneous primitive ideals of the ring of differential operators is finite. Furthermore, we give conditions for the algebra being simple.
Publié le : 2007-05-14
Classification:
Primitive ideals,
toric variety,
ring of differential operators,
hypergeometric systems,
13N10,
13P99,
16W35,
16S32
@article{1176734751,
author = {Saito, Mutsumi},
title = {Primitive ideals of the ring of differential operators on an affine toric variety},
journal = {Tohoku Math. J. (2)},
volume = {59},
number = {1},
year = {2007},
pages = { 119-144},
language = {en},
url = {http://dml.mathdoc.fr/item/1176734751}
}
Saito, Mutsumi. Primitive ideals of the ring of differential operators on an affine toric variety. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp. 119-144. http://gdmltest.u-ga.fr/item/1176734751/