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 Stiefel-Whitney classes of the representations of the orthogonal groups.
@article{JOLT_2021_31_1_a14,
author = {Jyotirmoy Ganguly and Rohit Joshi},
title = {Spinorial {Representations} of {Orthogonal} {Groups}},
journal = {Journal of Lie Theory},
pages = {265--286},
year = {2021},
volume = {31},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a14/}
}
TY - JOUR
AU - Jyotirmoy Ganguly
AU - Rohit Joshi
TI - Spinorial Representations of Orthogonal Groups
JO - Journal of Lie Theory
PY - 2021
SP - 265
EP - 286
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a14/
ID - JOLT_2021_31_1_a14
ER -
%0 Journal Article
%A Jyotirmoy Ganguly
%A Rohit Joshi
%T Spinorial Representations of Orthogonal Groups
%J Journal of Lie Theory
%D 2021
%P 265-286
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a14/
%F JOLT_2021_31_1_a14
