International Journal of Theoretical Physics

, Volume 50, Issue 4, pp 974–981 | Cite as

\(\mathcal{PT}\) Invariant Complex E8 Root Spaces

Article

Abstract

We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E8-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concrete application of this construction we propose new generalisations of Calogero-Moser-Sutherland models and affine Toda field theories based on the invariant complex root spaces and deformed complex simple roots, respectively.

Keywords

\(\mathcal{PI}\)-symmetry Non-Hermitian Hamiltonians Perturbed Ising model 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre for Mathematical ScienceCity University LondonLondonUK

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