Coxeter cones and their h-vectors

Coxeter cones are formed by intersecting the nonnegative sides of a collection of root hyperplanes in some root system. They are shellable subcomplexes of the Coxeter complex, and their h-vectors record the distribution of descents among their chambers. We identify a natural class of �graded� Coxeter cones with the property that their h-vectors are symmetric and unimodal, thereby generalizing recent theorems of Reiner�Welker and Branden about the Eulerian polynomials of graded partially ordered sets.

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