The special unitary group sp(n) is a mathematical concept that describes symmetries in an even-dimensional space, specifically the symmetries of a symplectic vector space. It consists of linear transformations that preserve a symplectic form, which is crucial in areas like Riemannian geometry and physics, particularly in Hamiltonian mechanics. Understanding sp(n) is essential for classifying holonomy groups and analyzing the geometric structures associated with Riemannian manifolds.
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