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It is shown that the isometry group of the de Sitter spacetime includes twodifferent three-dimensional Abelian subgroups which transform betweenthemselves through a discrete isometry corresponding to the time reversal inthe five-dimensional Minkowski spacetime embedding the de Sitter one. Theeigenfunctions of the generators of these Abelian subgroups form two differentsets of quantum modes correlated by the mentioned isometry.

Discrete O(1,4) transformations and new scalar quantum modes on the de Sitter spacetime