Cone In Rn Research Articles

Weyl Chambers and Standard Monomial Theory for Poset Lattice Cones

By a lattice cone, we mean the intersection with Z of a convex polyhedral cone in Rn. It is a semigroup under vector addition. If the faces of the cone are defined by rational linear functionals, the semigroup will be finitely generated. The associated semigroup algebra is then a finitely generated, hence Noetherian, commutative algebra [BH]. The varieties associated to these algebras are affine toric varieties [Fu].