21 research outputs found
Root polytopes and abelian ideals
We study the root polytope of a finite irreducible
crystallographic root system using its relation with the abelian ideals
of a Borel subalgebra of a simple Lie algebra with root system . We
determine the hyperplane arrangement corresponding to the faces of codimension
2 of and analyze its relation with the facets of . For of type or , we show that the orbits of some
special subsets of abelian ideals under the action of the Weyl group
parametrize a triangulation of . We show that this
triangulation restricts to a triangulation of the positive root polytope
.Comment: 41 pages, revised version, accepted for publication in Journal of
Algebraic Combinatoric