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 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: reviewed
- Last edited by Jennifer Paulhus on 2022-07-19 14:30:14

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**History:**(expand/hide all)

- 2022-07-19 14:30:14 by Jennifer Paulhus (Reviewed)
- 2021-10-19 02:54:49 by David Roe
- 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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