  We study the central hyperplane arrangement whose hyperplanes are the
vanishing loci of the weights of the first and the second fundamental
representations of $\mathfrak{gl}_n$ restricted to the dual fundamental Weyl
chamber. We obtain generating functions that count flats and faces of a given
dimension. This counting is interpreted in physics as the enumeration of the
phases of the Coulomb and mixed Coulomb-Higgs branches of a five dimensional
gauge theory with 8 supercharges in presence of hypermultiplets transforming in
the fundamental and antisymmetric representation of a U(n) gauge group as
described by the Intriligator-Morrison-Seiberg superpotential.
