McKay quivers of small finite subgroups of $GL(2,\mathbb{C})$

TL;DR

This paper explicitly computes the McKay quivers for small finite subgroups of GL(2,C), revealing their rich symmetry and structure, and compares these with known results for subgroups of SU(2).

Contribution

It provides explicit calculations of McKay quivers for small finite subgroups of GL(2,C) using character theory, expanding understanding beyond SU(2) cases.

Findings

Rich symmetry and combinatorial structure of the quivers

Comparison with classical McKay quivers of SU(2) subgroups

Explicit examples illustrating the structure

Abstract

We explicitly compute the McKay quivers of small finite subgroups of $GL(2,\mathbb{C})$ relative to the natural representation, using character theory and the McKay quivers of finite subgroups of $SU(2)$. We present examples that shows the rich symmetry and combinatorial structure of these quivers. We compare our results with the MacKay quivers computed by Auslander and Reiten.