Journal of Lie Theory

no. 1
Spinorial Representations of Orthogonal Groups
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 265-286
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.
DOI: 10.5802/jolt.1170
Classification: 22E41, 22E47, 57R20
Keywords: Orthogonal group, spinorial representation, Stiefel-Whitney class, highest weight 
@article{JOLT_2021_31_1_a14,
     author = {J. Ganguly and R. Joshi},
     title = {Spinorial {Representations} of {Orthogonal} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {265--286},
     year = {2021},
     volume = {31},
     number = {1},
     doi = {10.5802/jolt.1170},
     zbl = {1472.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1170/}
}
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J. Ganguly; R. Joshi. Spinorial Representations of Orthogonal Groups. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 265-286. doi: 10.5802/jolt.1170

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