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Let $\rho:G\to\GL_n(\C)$ be an irreducible complex group representation. Then $\rho$ is one of three types:

1. **Real** if $\rho$ is conjugate to a representation $G\to \GL_n(\R)$
2. **Complex** if some character value $\textrm{Tr}(\rho(g))$ is not all contained in $\R$
3. **Quaternionic** if the character values are all real but the representation is not conjugate to a real representation.

The type of the representation can be computed via its Frobenius-Schur indicator.

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• Review status: beta
• Last edited by John Jones on 2020-12-17 09:32:53
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