
Journal of Lie Theory 31 (2021), No. 1, 265286 Copyright Heldermann Verlag 2021 Spinorial Representations of Orthogonal Groups Jyotirmoy Ganguly The Institute of Mathematical Sciences, Chennai 600113, TamilNadu, India jyotirmoy.math@gmail.com Rohit Joshi Pune 411004, Maharashtra, India rohitsj@students.iiserpune.ac.in [Abstractpdf] Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, 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 criteria for whether an orthogonal representation $\pi\colon G\to \text{O}(V)$ lifts to $\text{Pin}(V)$ in terms of the highest weights of $\pi$ and also in terms of character values. From these criteria we compute the first and second StiefelWhitney classes of the representations of the orthogonal groups. Keywords: Orthogonal group, spinorial representation, StiefelWhitney class, highest weight. MSC: 22E41, 22E47, 57R20. [ Fulltextpdf (184 KB)] for subscribers only. 