Representation theory MOC

McKay graph

Let be a finite group and be of characteristic not dividing , and be representative simple -modules, where we denote the trivial irrep . The McKay graph of a -module is a pseudomultidigraph such that #m/def/rep2

• the vertices of are the irreps ;
• there exists an edge for every occurrence of in the decomposition of .¹

The McKay matrix is then the adjacency matrix of , and we have

Properties

• Spectrum of a McKay graph

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