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A Poisson Structure on Compact Symmetric Spaces

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Abstract

We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721-0089, USA

    P. Foth

  2. Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China

    J.-H. Lu

Authors
  1. P. Foth
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  2. J.-H. Lu
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Correspondence to P. Foth.

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Communicated by L. Takhtajan

Acknowledgements We thank Sam Evens for many useful discussions. The first author was partially supported by NSF grant DMS-0072520. The second author was partially supported by NSF(USA) grants DMS-0105195 and DMS-0072551 and by the HHY Physical Sciences Fund at the University of Hong Kong.

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Foth, P., Lu, JH. A Poisson Structure on Compact Symmetric Spaces. Commun. Math. Phys. 251, 557–566 (2004). https://doi.org/10.1007/s00220-004-1178-4

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