McKay quivers and extended Dynkin diagrams

Auslander, Maurice; Reiten, Idun

doi:10.1090/S0002-9947-1986-0814923-X

McKay quivers and extended Dynkin diagrams
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by Maurice Auslander and Idun Reiten PDF

Trans. Amer. Math. Soc. 293 (1986), 293-301 Request permission

Abstract:

Let $k$ be an algebraically closed field and $G$ a finite nontrivial group whose order is not divisible by the characteristic of $k$. Associated with an $m$-dimensional representation of $G$ is the McKay quiver, whose vertices correspond to the irreducible representations of $G$. We show that if $m = 2$, then the underlying graph of the separated McKay quiver is a finite union of extended Dynkin diagrams.

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