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A finite crossed module is a 4-tuple $$(G_1,G_2,\delta: G_2 \to G_1, \alpha: G_1 \to Aut(G_2))$$ satisfying certain compatible conditions, where the $G_i$ are finite groups and the maps are group homo …

$\DeclareMathOperator\Rep{Rep}\DeclareMathOperator\rank{rank}$Let $G$ be a finite group, and $C=\Rep(G)$ be the monoidal category of complex finite-dimensional representations of $G$. As $C$ is finite …

TL; DR. In representation theory, it's nice to decompose a given representation into smaller ones. One technique is by utilizing extra symmetries. Explicit examples come from compact groups, and I won …

Let $G$ be a finite group and $D(G)$ its quantum double. Its finite dimensional complex representations are classified in this Dijkgraaf et al. Quasi-Quantum Groups Related To Orbifold Models. However …

This is a study note that spells out @Konstantinos's answer explicitly. Preface Our goal is to classify all finite dimensional representations over the complex number field for the quantum double …

This is my study note that spells out @Adrien 's answer to 1) and 2). As suggested by @Adrien, we will follow Kassel's Quantum Groups, mainly chapter XIII.5. It is a very detailed account. Explicit e …

Let $G$ be a finite group and $D(G)$ its quantum double. As in my previous question, a typical irreducible representation (finite dimensional over $\mathbb{C}$) is labeled by $(\theta,\pi)$, where $\t …