Algebras Generated by Reciprocals of Linear Forms

✍ Scribed by Hiroaki Terao

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 97 KB
• Volume: 250
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9121

✦ Synopsis

Let be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C of rational functions generated by 1/α α ∈

. Then the ring ∂ V of differential operators with constant coefficients naturally acts on C

. We study the graded ∂ V -module structure of C

. We especially find standard systems of minimal generators and a combinatorial formula for the Poincaré series of C

. Our proofs are based on a theorem by Brion-Vergne [4] and results by .