Spinorial Representations of Orthogonal Groups

Jyotirmoy Ganguly; Rohit Joshi

paper

Spinorial Representations of Orthogonal Groups

arXiv:2003.06636

Abstract

Let $G$ be a real compact Lie group, such that $G = G^{0} ⋊ C_{2}$ , with $G^{0}$ simple. Here $G^{0}$ is the connected component of $G$ containing the identity and $C_{2}$ is the cyclic group of order $2$ . We give a criterion for whether an orthogonal representation $π : G \to O (V)$ lifts to $Pin (V)$ in terms of the highest weights of $π$ . We also calculate the first and second Stiefel-Whitney classes of the representations of the Orthogonal groups.