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It is shown that any symplectic $2n\times 2n$-matrix, whose entries arecomplex holomorphic functions on a reduced Stein space, can be decomposed intoa finite product of elementary symplectic matrices if and only if it isnull-homotopic. Moreover, if this is the case, the number of factors can bebounded by a constant depending only on $n$ and the dimension of the space.

Holomorphic Factorization of Mappings into the Symplectic Group