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ON DIFFERENTIAL EQUATIONS OF VON GEHLEN AND ROAN

Published online by Cambridge University Press:  01 February 2009

ETSURO DATE*
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University e-mail: [email protected]
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Abstract

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Polynomials appearing in the description of ground states of superintegrable chiral Potts models are shown to satisfy a special class of generalised hypergeometric differential equations after a simple modification. This proves a conjecture of von-Gehlen and Roan.

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Albertini, G., McCoy, B. M. and Perk, J. H. H., Eigenvalue spectrum of the superintegrable chiral Potts model, in Advanced studies in pure mathematics, vol. 19 (Kinokuniya Academic, Tokyo, 1989), 155.Google Scholar
2.Baxter, R. J., The superintegrable chiral Potts model, Phys. Lett. A, 133, 185–189.Google Scholar
3.von Gehlen, G., Onsager's algebra and partially orthogonal polynomials, Int. J. Mod. Phys. B, 16 (2002), 21292136.Google Scholar
4.von Gehlen, G. and Roan, S. S., The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials, in Integrable structure of exactly solvable two-dimensional models of quantum field theory, vol. 35 (Pakuliak, S. and von Gehlen, G., Editors) (Kluwer Academic Publisher, Dordrecht, 2001), 155172.Google Scholar
5.Okubo, K., Takano, K. and Yoshida, S., A connection problem for the generalized hypergeometric equation. Funkcial. Ekvac. 31 (1988), 483495.Google Scholar
6.Roan, S. S., Structure of certain Chebyshev-type polynomials in Onsager's algebra representation, J. Comput. Appl. Math. 202 (2007), 88-1-4.Google Scholar