If $G$ is a finite group and $\chi$ is the character of an irreducible complex representation of $G$, then its **Frobenius-Schur indicator** is given by
\[ \frac{1}{|G|}\sum_{g\in G} \chi(g^2).\]
It is $0$, $1$, or $-1$ depending on whether the representation is of complex type, real type, or quaternionic type respectively.

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**Knowl status:**

- Review status: reviewed
- Last edited by Alina Bucur on 2019-05-02 20:58:32

**Referred to by:**

- lmfdb/artin_representations/templates/artin-representation-index.html (line 99)
- lmfdb/artin_representations/templates/artin-representation-search.html (line 44)
- lmfdb/artin_representations/templates/artin-representation-search.html (line 72)
- lmfdb/number_fields/templates/nf-show-field.html (line 268)

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

- 2019-05-02 20:58:32 by Alina Bucur (Reviewed)
- 2019-05-02 20:55:22 by Alina Bucur
- 2013-09-12 01:33:18 by John Jones

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