English

The magic square of reflections and rotations

Group Theory 2024-01-23 v2 Rings and Algebras

Abstract

We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in O(3)O(3). We also consider this magic square of reflections and rotations in the framework of Clifford algebras: we give an interpretation using (s)pin groups and explore these groups in small dimensions.

Keywords

Cite

@article{arxiv.1806.04600,
  title  = {The magic square of reflections and rotations},
  author = {Ragnar-Olaf Buchweitz and Eleonore Faber and Colin Ingalls},
  journal= {arXiv preprint arXiv:1806.04600},
  year   = {2024}
}

Comments

27 pages, V2: final version

R2 v1 2026-06-23T02:27:33.439Z