{ "id": "1806.04600", "version": "v1", "published": "2018-06-12T15:21:58.000Z", "updated": "2018-06-12T15:21:58.000Z", "title": "The magic square of reflections and rotations", "authors": [ "Ragnar-Olaf Buchweitz", "Eleonore Faber", "Colin Ingalls" ], "comment": "27 pages", "categories": [ "math.GR", "math.RA" ], "abstract": "We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in $O(3)$. 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.", "revisions": [ { "version": "v1", "updated": "2018-06-12T15:21:58.000Z" } ], "analyses": { "subjects": [ "20F55", "15A66", "11E88", "14E16" ], "keywords": [ "magic square", "complex reflection groups", "coxeters work implies", "real reflection groups", "clifford algebras" ], "note": { "typesetting": "TeX", "pages": 27, "language": "en", "license": "arXiv", "status": "editable" } } }