Abstract
Similarly as in the theory of Kac-Moody algebras, affine extensions of the non-crystallographic Coxeter groupsH k, (k=2, …, 4) can be derived via an appropriate extension of the Cartan matrix. These groups lead to novel applications in the theory of quasicrystals and integrable models. In the former case, a new model for quasicrystals with five-fold symmetries could be established; in the latter case, subgroups have been used to obtain a Calogero model related to a non-integrally laced group.
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Financial support through a European-Union Marie Curie fellowship is gratefully acknowledged.
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Twarock, R. An affine extension of non-crystallographic Coxeter groups with applications in the theory of quasicrystals and integrable systems. Czech J Phys 51, 400–408 (2001). https://doi.org/10.1023/A:1017506026236
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DOI: https://doi.org/10.1023/A:1017506026236