See also compact symplectic group.
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This Lie group is the analog of the unitary group as one passes from the complex numbers to the quaternions.
The quaternionic unitary group is the group of quaternion-unitary transformations of . It is also called the compact symplectic group, since both it and the symplectic group are real forms of the complex Lie group , and it is the compact form.
A Riemannian manifold of dimension is called a quaternion-Kähler manifold if its holonomy group is a subgroup of the quotient group Sp(n).Sp(1) of the direct product group . If it is even a subgroup of just the factor, then it is called a hyperkähler manifold.
Howard Georgi, §26 in: Lie Algebras In Particle Physics, Westview Press (1999), CRC Press (2019) [doi:10.1201/9780429499210]
Quaternionic groups (pdf)
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