McKay graph

Summary

In mathematics, the McKay graph of a finite-dimensional representation $V$ of a finite group $G$ is a weighted quiver encoding the structure of the representation theory of $G$. Each node represents an irreducible representation of $G$. If $\chi_{i}, \chi_{j}$ are irreducible representations of $G$, then there is an arrow from $\chi_{i}$ to $\chi_{j}$ if and only if $\chi_{j}$ is a constituent of the tensor product $V\otimes\chi_i.$ Then the weight $n_{ij}$ of the arrow is the number of times this constituent appears in $V \otimes\chi_i.$ For finite subgroups $H$ of $\text{GL}(2, \mathbb{C}),$ the McKay graph of $H$ is the McKay graph of the defining 2-dimensional representation of $H$.