Mixed-symmetry fields in de Sitter space: a group theoretical glance
Résumé
We derive the characters of all unitary irreducible representations of the (d+1)-dimensional de Sitter spacetime isometry algebra $ \mathfrak{so}\left(1,\kern0.5em d+1\right) $ , and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime.
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