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The de Sitter group and its presence at the late-time boundary
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Our main goal here is to provide an introduction on some of the well established properties of the representation theory of SO(d+1,1), for those considering to think on physical problems set in de Sitter space in terms of these representations. With this purpose we review two intertwining maps, the map G that is used in constructing a well defined inner product for the complementary series representations and the map Q that is involved in constructing composite representations. We give explicit examples from the late-time boundary of de Sitter on the practical use of the complementary series inner product and in building a tensor product representation from unitary principal series irreducible representations.
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A discrete series gauge field at the late-time boundary of $dS_4$
Both Δ=1 and Δ=2 late-time Maxwell operators on planar dS4 furnish the photon unitary discrete series of SO(4,1), which splits into opposite-helicity summands via self-dual field-strength sectors.
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