The geometry of special symplectic representations
| Autor: | Marcus J. Slupinski, Robert J. Stanton |
|---|---|
| Přispěvatelé: | Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Ohio State University [Columbus] (OSU) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Subvariety Structure (category theory) Field (mathematics) 01 natural sciences MSC: 17B60 53A40 53D05 0103 physical sciences Lie algebra FOS: Mathematics 0101 mathematics Algebraic number Representation Theory (math.RT) Mathematics Algebra and Number Theory special symplectic representations [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] 010102 general mathematics 16. Peace & justice coisotropic orbits [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] Differential Geometry (math.DG) Conic section [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Mathematics - Symplectic Geometry Metric (mathematics) Symplectic Geometry (math.SG) 010307 mathematical physics Mathematics - Representation Theory Symplectic geometry special metrics |
| Popis: | We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and alternating three forms in six dimensions. All nonzero orbits are coisotropic and the covariants satisfy relations generalising classical identities of Eisenstein and Mathews. The main algebraic result is that suitably generic elements of these representation spaces can be uniquely written as the sum of two elements of a naturally defined Lagrangian subvariety. We give universal explicit formulae for the summands and show how they lead to the existence of geometric structure on appropriate subsets of the representation space. Over the reals this structure reduces to either a conic, special pseudo-K\" ahler metric or a conic, special para-K\" ahler metric. 31pages |
| Databáze: | OpenAIRE |
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