A note on the representations of SO(1,d + 1)

Abstract

[Formula: see text] is the isometry group of [Formula: see text]-dimensional de Sitter spacetime ([Formula: see text]) and the conformal group of [Formula: see text]. This note gives a pedagogical introduction to the representation theory of [Formula: see text], from the perspective of de Sitter quantum field theory and using tools from conformal field theory. Topics include (1) the construction and classification of all unitary irreducible representations (UIRs) of [Formula: see text] and [Formula: see text], (2) the construction and classification of all UIRs of [Formula: see text] that describe integer-spin fields in [Formula: see text], (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of [Formula: see text] and (5) a comparison between UIRs of [Formula: see text] and [Formula: see text].