# The super Frobenius-Schur indicator and finite group gauge theories on pin$^-$ surfaces

12 Mar 2020 Ichikawa Takumi Tachikawa Yuji

It is well-known that the value of the Frobenius-Schur indicator $|G|^{-1} \sum_{g\in G} \chi(g^2)=\pm1$ of a real irreducible representation of a finite group $G$ determines which of the two types of real representations it belongs to, i.e. whether it is strictly real or quaternionic. We study the extension to the case when a homomorphism $\varphi:G\to \mathbb{Z}/2\mathbb{Z}$ gives the group algebra $\mathbb{C}[G]$ the structure of a superalgebra... (read more)

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• REPRESENTATION THEORY
• STRONGLY CORRELATED ELECTRONS
• HIGH ENERGY PHYSICS - THEORY
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