Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction

Research output: Contribution to journalArticlepeer-review


In this paper, we show that via a novel construction every rank-3 root system induces a root system of rank 4. In a Clifford algebra framework, an even number of successive Coxeter reflections yields - via the Cartan-Dieudonne theorem - spinors that describe rotations. In three dimensions these spinors themselves have a natural four-dimensional Euclidean structure, and discrete spinor groups can therefore be interpreted as 4D polytopes. In fact, these polytopes have to be root systems, thereby inducing Coxeter groups of rank 4. For the corresponding case in two dimensions, the groups I_2(n) are shown to be self-dual.
Original languageEnglish
Article number012027
Number of pages7
JournalJournal of Physics: Conference Series
Issue numberconference 1
Early online date13 Apr 2015
Publication statusPublished - Jul 2015

Bibliographical note

This content is made available by the publisher under a Creative Commons CC-BY Licence.

Cite this