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 type of the representation is complex type, real, or quaternionic respectively.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2020-12-17 09:30:37

**Referred to by:**

- group.representation.type
- lmfdb/artin_representations/main.py (line 239)
- lmfdb/artin_representations/main.py (line 598)
- lmfdb/artin_representations/main.py (line 733)
- lmfdb/artin_representations/templates/artin-representation-galois-orbit.html (line 11)
- lmfdb/artin_representations/templates/artin-representation-show.html (line 11)
- lmfdb/number_fields/templates/nf-show-field.html (line 282)

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

- 2020-12-17 09:30:37 by John Jones (Reviewed)
- 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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