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A. J. Di Scala Dipartimento di Matematica, Politecnico di Torino Torino, Italy antonio.discala@polito.it A. Loi G. Roos

The symplectic duality of Hermitian symmetric spaces
In this talk I describe the symplectic duality map : M n Cn of an Hermitian Symmetric Space M . This map was introduced in [DL]. The main property of is to be a bi-symplectorphism, namely, 0 = hyp and F S = 0 , where 0 is the flat symplectic form of M (regarded as a bounded domain of Cn ), hyp is the hyperbolic form on M and F S is the Fubini-Study form on the affine chart Cn CP n . Then I will discuss the unicity problem of such a map, i.e. to what extent this map is unique. This last part is based on the work [DLR]. References [DL] Di Scala, A.J. and Loi, A., Symplectic Duality of Symmetric Spaces, arXiv math.DG/0603141. [DLR] Di Scala, A.J. ; Loi, A. and Roos, G. The unicity of the symplectic duality, arXiv math.DG/0707.2125

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