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Non-compact symmetric spaces and the Toda molecule equations

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It has been shown by Olshanetsky and Perelomov that the Toda molecule equations associated with any Lie groupG describe special geodesic motions on the Riemannian non-compact symmetric space which is the quotient of the normal real form ofG, G N, by its maximal compact subgroup. This is explained in more detail and it is shown that the “fundamental Poisson bracket relation” involving the Lax operatorA and leading to the Yang-Baxter equation and integrability properties is a direct consequence of the fact that the Iwasawa decomposition forG N endows the symmetric space with a hidden group theoretic structure.

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Authors and Affiliations

  1. The Blackett Laboratory, Imperial College, SW7 2BZ, London, England

    L. A. Ferreira & D. I. Olive

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  1. L. A. Ferreira
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  2. D. I. Olive
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Communicated by A. Jaffe

Supported by CNP q (Brasil)

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Ferreira, L.A., Olive, D.I. Non-compact symmetric spaces and the Toda molecule equations. Commun.Math. Phys. 99, 365–384 (1985). https://doi.org/10.1007/BF01240353

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  • DOI: https://doi.org/10.1007/BF01240353

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