English

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

Representation Theory 2025-08-01 v1 Combinatorics Group Theory

Abstract

We explicitly compute the McKay quivers of small finite subgroups of GL(2,C)GL(2,\mathbb{C}) relative to the natural representation, using character theory and the McKay quivers of finite subgroups of SU(2)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.

Keywords

Cite

@article{arxiv.2507.23171,
  title  = {McKay quivers of small finite subgroups of $GL(2,\mathbb{C})$},
  author = {José Luis Cisneros-Molina and Meral Tosun},
  journal= {arXiv preprint arXiv:2507.23171},
  year   = {2025}
}

Comments

37 pages, 10 tables, 11 figures