McKay correspondence

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 ${\displaystyle \chi _{i},\chi _{j}}$ are irreducible representations of G then there is an arrow from ${\displaystyle \chi _{i}}$ to ${\displaystyle \chi _{j}}$ if and only if ${\displaystyle \chi _{j}}$ is a constituent of the tensor product ${\displaystyle V\otimes \chi _{i}}$. Then the weight n_ij of the arrow is the number of times this constituent appears in ${\displaystyle V\otimes \chi _{i}}$. For finite subgroups H of GL(2, C), the McKay graph of H is the McKay graph of the canonical representation of H.

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