An affine extension of non-crystallographic Coxeter groups with applications in the theory of quasicrystals and integrable systems

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JournalCzechoslovak journal of physics
DatePublished - 1 Apr 2001
Issue number4
Volume51
Number of pages9
Pages (from-to)400-408
Original languageEnglish

Abstract

Similarly as in the theory of Kac-Moody algebras, affine extensions of the non-crystallographic Coxeter groups H-k, (k = 2, ..., 4) can be derived via an appropriate extension of :he 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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