Symplectic Duality of Symmetric Spaces

With the aid of the theory of Jordan triple systems, we construct an explicit bi-symplectomorphism between a Hermitian symmetric space of non-compact type and the complex Euclidean space equipped with both the flat Kaehler-form and the Fubini-Study form. Our symplectomorphism is an explicit version of the symplectomorphism between Kaehler manifolds with non positive radial curvature and complex Euclidean space, whose existence was proved by Dusa McDuff. As a byproduct we get an interesting characterization of the Bergman form on a Hermitian symmetric space in terms of its restriction to classical Hermitian symmetric spaces of noncompact type.

(This paper has appeared in Adv. Math. 217 (2008), 2336 -- 2352)

sympduality.pdf (217K)

Antonio J. Di Scala < antonio.discala@polito.it >

Andrea Loi < loi@unica.it >