Affine extensions of non-crystallographic Coxeter groups induced by projection

Details Affine extensions of non-crystallographic Coxeter groups induced by projection Affine extensions of non-crystallographic Coxeter groups induced by projection

2011-10-24

arxiv.org/abs/1110.5228v1

Physics

Mathematical Physics

23 pages, 9 figures

Scientific paper

In this paper, we show that affine extensions of non-crystallographic Coxeter groups can be derived via Coxeter-Dynkin diagram foldings and projections of the root systems E_8, D_6 and A_4. Using the known extensions for these root systems, we induce affine extensions of the non-crystallographic groups H_4, H_3 and H_2, and show that they correspond to Kac-Moody-type extensions considered in Dechant et al. This class of extensions was motivated by physical applications in icosahedral systems in biology (viruses), physics (quasicrystals) and chemistry (fullerenes); the connection with the affine extension of E_8 derived here suggests potential for high energy physics applications. The invertibility of the projection suggests a generalisation of Cartan matrices by relaxing some of the usual requirements.

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