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Incidence geometry in a Weyl chamber II: SL

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2020Embargo end date: 01 Jan 2015Publisher:Elsevier BVJournal:Advances in Applied Mathematics, volume 119, page 102,049 (issn: 0196-8858,

Authors: Alfred G. Noël; Ravi Jagadeesan; Steven Glenn Jackson; Mboyo Esole;

doi: 10.1016/j.aam.2020.102049 , 10.1016/j.aam.2020.102048 , 10.48550/arxiv.1508.03038 , 10.48550/arxiv.1601.05070

arXiv: http://arxiv.org/abs/1508.03038 , http://arxiv.org/abs/1601.05070

Incidence geometry in a Weyl chamber II: SL

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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.

25 pages, 6 figures

Related Organizations

University of Massachusetts System
United States
Harvard University
United States

Keywords

High Energy Physics - Theory, 05E10, 52C35, 05A15, 17B10, 17B81, High Energy Physics - Theory (hep-th), FOS: Mathematics, Mathematics - Combinatorics, FOS: Physical sciences, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory

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