We study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of 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.2010 Mathematics Subject Classification. 05E10, 52C35, 05A15, 17B10, 17B81.
We compute the irreducible components and relative invariants of certain prehomogeneous spaces arising in the theory of nilpotent orbits in complex reductive Lie algebras. 2005 Elsevier Inc. All rights reserved.
In this paper we give a classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie groups of inner type. We use a lemma of Takuya Ohta and some information from the work of Dragomir Djoković to construct a simple algorithm which allows us to decide the admissiblity of a given orbit.
In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra g under the action of its adjoint group. Our classification generalizes the Bala-Carter classification of the nilpotent orbits of complex semisimple Lie algebras. Our theory takes full advantage of the work of Kostant and Rallis on p C , the "complex symmetric space associated with g". The Kostant-Sekiguchi correspondence, a bijection between nilpotent orbits in g and nilpotent orbits in p C , is also used. We identify a fundamental set of noticed nilpotents in p C and show that they allow us to recover all other nilpotents. Finally, we study the behaviour of a principal orbit, that is an orbit of maximal dimension, under our classification. This is not done in the other classification schemes currently available in the literature.
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