Incidence geometry in a Weyl chamber II: SL
Copyright policy )Incidence geometry in a Weyl chamber II: SL
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
- University of Massachusetts System United States
- Harvard University United States
- University of Massachusetts Boston United States
- UNIVERSITY OF MASSACHUSETTS United States
roots, High Energy Physics - Theory, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Lie algebra, Exact enumeration problems, generating functions, FOS: Physical sciences, extreme rays, weights lattice, poset, FOS: Mathematics, Mathematics - Combinatorics, Representation Theory (math.RT), hyperplane arrangement, Applications of Lie (super)algebras to physics, etc., Weyl chambers, root systems, representation theory, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), 05E10, 52C35, 05A15, 17B10, 17B81, High Energy Physics - Theory (hep-th), Combinatorial aspects of representation theory, Combinatorics (math.CO), weights, Mathematics - Representation Theory
roots, High Energy Physics - Theory, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Lie algebra, Exact enumeration problems, generating functions, FOS: Physical sciences, extreme rays, weights lattice, poset, FOS: Mathematics, Mathematics - Combinatorics, Representation Theory (math.RT), hyperplane arrangement, Applications of Lie (super)algebras to physics, etc., Weyl chambers, root systems, representation theory, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), 05E10, 52C35, 05A15, 17B10, 17B81, High Energy Physics - Theory (hep-th), Combinatorial aspects of representation theory, Combinatorics (math.CO), weights, Mathematics - Representation Theory
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