Conformal symmetries of the super Dirac operator

• Kevin Coulembier ^[1] ; Hendrik De Bie ^[1]
  1. [1] Ghent University

     Ghent University

     Arrondissement Gent, Bélgica

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 2, 2015, págs. 373-410
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, the Dirac operator, acting on super functions with values in super spinor space, is defined along the lines of the construction of generalized Cauchy--Riemann operators by Stein and Weiss. The introduction of the superalgebra of symmetries osp(m|2n) is a new and essential feature in this approach. This algebra of symmetries is extended to the algebra of conformal symmetries osp(m+1,1|2n). The kernel of the Dirac operator is studied as a representation of both algebras. The construction also gives an explicit realization of the Howe dual pair osp(1|2)×osp(m|2n)⊂osp(m+4n|2m+2n). Finally, the super Dirac operator gives insight into the open problem of classifying invariant first order differential operators in super parabolic geometries.