---
tag: 1H7X0R5PSQ
kind: concept
name: McKay graph
aliases: [mckay-correspondence]
sources:
  - wikipedia: en:34080241@r1366267521
    locator: McKay graph
    note: adopted
    mention: wikipedia://en/34080241
    sections: [Summary]
same_as:
  wikidata: Q6801707
  wikipedia: McKay graph
inventory: [NMWZQG6VVC]
---

## 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|0BF2DE2SYK]] $V\otimes\chi_i.$ Then the weight $n_{ij}$ of the arrow is the number of times this constituent appears in $V \otimes\chi_i.$ For finite [[subgroups|0X1JXT47GA]] $H$ of $\text{GL}(2, \mathbb{C}),$ the McKay graph of $H$ is the McKay graph of the defining 2-dimensional representation of $H$.