Tohoku Mathematical Journal
2007
March
SECOND SERIES VOL. 59, NO. 1

Tohoku Math. J.
59 (2007), 119-144

Title PRIMITIVE IDEALS OF THE RING OF DIFFERENTIAL OPERATORS ON AN AFFINE TORIC VARIETY

Author Mutsumi Saito

(Received April 19, 2006, revised September 11, 2006)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 13N10; Secondary 13P99, 16W35, 16S32.

Key words and phrases. Primitive ideals, toric variety, ring of differential operators, hypergeometric systems.

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