Quadratic initial ideals of root systems
Authors:
Hidefumi Ohsugi and Takayuki Hibi
Journal:
Proc. Amer. Math. Soc. 130 (2002), 19131922
MSC (2000):
Primary 13P10
Published electronically:
December 27, 2001
MathSciNet review:
1896022
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Abstract: Let be one of the root systems , , and and write for the set of positive roots of together with the origin of . Let denote the Laurent polynomial ring over a field and write for the affine semigroup ring which is generated by those monomials with , where if . Let denote the polynomial ring over and write for the toric ideal of . Thus is the kernel of the surjective homomorphism defined by setting for all . In their combinatorial study of hypergeometric functions associated with root systems, Gelfand, Graev and Postnikov discovered a quadratic initial ideal of the toric ideal of . The purpose of the present paper is to show the existence of a reverse lexicographic (squarefree) quadratic initial ideal of the toric ideal of each of , and . It then follows that the convex polytope of the convex hull of each of , and possesses a regular unimodular triangulation arising from a flag complex, and that each of the affine semigroup rings , and is Koszul.
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Additional Information
Hidefumi Ohsugi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560–0043, Japan
Email:
ohsugi@math.sci.osakau.ac.jp
Takayuki Hibi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560–0043, Japan
Email:
hibi@math.sci.osakau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993901064115
PII:
S 00029939(01)064115
Received by editor(s):
August 8, 2000
Received by editor(s) in revised form:
January 29, 2001
Published electronically:
December 27, 2001
Communicated by:
John R. Stembridge
Article copyright:
© Copyright 2001
American Mathematical Society
