Discrete O(1,4) transformations and new scalar quantum modes on the de   Sitter spacetime
  It is shown that the isometry group of the de Sitter spacetime includes two different three-dimensional Abelian subgroups which transform between themselves through a discrete isometry corresponding to the time reversal in the five-dimensional Minkowski spacetime embedding the de Sitter one. The eigenfunctions of the generators of these Abelian subgroups form two different sets of quantum modes correlated by the mentioned isometry. 
Ion I. Cotaescu
gr-qc hep-th