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

- **Real** if $\rho$ is conjugate to a representation $G\to \GL_n(\R)$
- **Complex** if some character value $\textrm{Tr}(\rho(g))$ is not all contained in $\R$
- **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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**Knowl status:**

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

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- 2020-12-17 09:32:53 by John Jones
- 2020-12-17 09:25:57 by John Jones
- 2020-12-17 09:24:56 by John Jones

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