Searching for discrete series representations at the late-time boundary of de Sitter

Abstract: The group $SO(d+1,1)$ makes an appearance both as the conformal group of Euclidean space in $d$ dimensions and as the isometry group of de Sitter spacetime in $d+1$ dimensions. While this common feature can be taken as a hint towards holography on de Sitter space, understanding the representation theory has importance for cosmological applications where de Sitter spacetime is relevant. Among the categories of $SO(d+1,1)$ unitary irreducible representations, discrete series is important in physical applications because they are expected to capture gauge fields. However, they are also the most difficult ones to recognize in field theoretical examples compared to representations from the other categories. Here we point towards some examples where we are able to recognize discrete series representations from fields on de Sitter and highlight some of the properties of these representations.