MathGloss

The complex symplectic group $\text{Sp}(2n,\mathbb C)$ is the group of $2n\times 2n$ complex-valued matrices that preserve the form $\omega$ as in the definition of the real symplectic group.

This group is a matrix Lie group because it is a subgroup of the general linear group $\text{GL}(n,\mathbb C)$.

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