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

SO(1,d + 1) is the isometry group of (d + 1)-dimensional de Sitter spacetime (dSd+1) and the conformal group of ℝd. This note gives a pedagogical introduction to the representation theory of SO(1,d + 1), 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 SO(1, 2) and SL(2, ℝ), (2) the construction and classification of all UIRs of SO(1,d + 1) that describe integer-spin fields in dSd+1, (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of SO(1,d + 1) and (5) a comparison between UIRs of SO(1,d + 1) and SO(2,d). [ABSTRACT FROM AUTHOR]