Could you help me for solving this: Let $Sp(n)$ be the group of linear transformations of $H^n$ such that preserve hermitian form $$\sum_{i=1}^n \overline{q_i}r_i,$$ that $H$ is the quaternions _ the non-commutative generalization of the complex numbers_, then we have $Sp(n)= Sp(2n,C)\cap U(2n)$, that $C$ is complex number.
[I mean : if $q= x+iy+ju+kv$ then $\overline{q}= x- iy-ju-kv$]