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arXiv · 1508.03038

Incidence Geometry in a Weyl Chamber I: $GL_n$

Mboyo Esole·Steven Glenn Jackson·Ravi Jagadeesan·Alfred G. Noël
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Abstract

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.

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BibTeXRIS

Mboyo Esole, Steven Glenn Jackson, Ravi Jagadeesan, Alfred G. Noël. 2015-08-12. Incidence Geometry in a Weyl Chamber I: $GL_n$. https://arxiv.org/abs/1508.03038

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