  $\text{SO}(1, d+1)$ is the isometry group of $(d+1)$-dimensional de Sitter
spacetime $\text{dS}_{d+1}$ and the conformal group of $\mathbb{R}^{d}$. This
note gives a pedagogical introduction to the representation theory of
$\text{SO}(1, d+1)$, 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
$\text{SO}(1,2)$ and $\text{SL}(2,\mathbb R)$, (2) the construction and
classification of all UIRs of $\text{SO}(1,d+1)$ that describe integer-spin
fields in $\text{dS}_{d+1}$, (3) a physical framework for understanding these
UIRs, (4) the definition and derivation of Harish-Chandra group characters of
$\text{SO}(1,d+1)$, and (5) a comparison between UIRs of $\text{SO}(1, d+1)$
and $\text{SO}(2,d)$.
