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2009-01-01 - Article/Dans un journal avec peer-review - Anglais - 18 page(s)

Devchand C., Nuyts Jean , Weingart G., "Matryoshka of Special Democratic Forms" in Communications in Mathematical Physics, 293, 2, 545-562

  • Edition : Springer Science & Business Media B.V.
  • Codes CREF : Physique des particules élémentaires (DI1221), Physique théorique et mathématique (DI1210)
  • Unités de recherche UMONS : Physique théorique et mathématique (S814)
Texte intégral :

Abstract(s) :

(Anglais) Special p-forms are forms which have components [FORMULA] equal to +1, -1 or 0 in some orthonormal basis. A p-form [FORMULA] is called democratic if the set of nonzero components [FORMULA] is symmetric under the transitive action of a subgroup of [FORMULA] on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P = p and D = d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G2-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form O in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.

Identifiants :
  • ISSN : 1432-0916
  • DOI : 10.1007/s00220-009-0939-5
  • EPRINT : arXiv:0812.3012 [math-ph]