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

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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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References

  1. V. Kac:Infinite Dimensional Lie Algebras, Cambridge University Press, Cambridge, 1985.

    MATH  Google Scholar 

  2. S. Kass, J.P.R.S. Moody, and R.V. Moody:Affine Lie Algebras, Weight Multiplicities and Branching Rules, Univ. of Calif. Press, Los Angeles, 1990.

    MATH  Google Scholar 

  3. J. Patera and R. Twarock:Affine extensions of non-crystallographic Coxeter groups and quasicrystals, Preprint CRM.

  4. Z. Masáková, J. Patera, and E. Pelantová: J. Phys. A: Math. Gen.31 (1998) 1539.

    Article  MATH  ADS  Google Scholar 

  5. J. Patera: inMathematics of Long Range Aperiodic Order (Ed. R.V. Moody), Kluwer, Dordrecht, 1997.

    Google Scholar 

  6. L. Chen, R.V. Moody, and J. Patera: inQuasicrystals and Discrete Geometry (Ed. J. Patera), Fields Institute Monograph Series, Amer. Math. Soc., 1998.

  7. R.V. Moody and J. Patera: J. Phys. A: Math. Gen.26 (1993) 2829.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. O. Haschke and W. Rühl:An exactly solvable model of the Calogero type for the icosahedral group, 1998 (hep-th/9811011).

  9. O. Haschke and W. Rühl:Is it possible to construct exactly solvable models?, 1998 (hep-th/9809152v3).

  10. R. Twarock: Phys. Lett. A275 (2000) 169.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. J.E. Humphreys:Reflection Groups and Coxeter Groups, Cambridge studies in advanced mathematics, Vol. 29, Cambridge Univ. Press, 1992.

  12. R. Twarock: inProc. XXIII Int. Coll. on Group Theoretical Methods in Physics, Dubna 2000, submitted to Phys. Atom. Nucl.

  13. J.-P. Antoine, L. Jacques, and R. Twarock: Phys. Lett. A261 (1999) 265.

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of York, YO10 5DD, York, England

    R. Twarock

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  1. R. Twarock
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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

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