Alcoved Polytopes II
This is the second of two papers where we study polytopes arising from affine Coxeter arrangements. Our results include a formula for their volumes, and also compatible definitions of hypersimplices, descent numbers and major index for all Weyl groups. We give a q-analogue of Weyl’s formula for the order of the Weyl group. For An, Cn and D4, we give a Gröobner basis which induces the triangulation of alcoved polytopes.
KeywordsConvex polytopes affine Weyl group hypersimplex
Mathematics Subject Classification (2010):Primary 52B Secondary 05A05 20F55
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