International Journal of Theoretical Physics

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

\(\mathcal{PT}\) Invariant Complex E 8 Root Spaces

  • Andreas FringEmail author
  • Monique Smith


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 E 8-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.


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


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre for Mathematical ScienceCity University LondonLondonUK

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