Tangent space of the symplectic group
= Tangent space of the symplectic group
At the identity, the symplectic Lie algebra consists of $X$ satisfying $X^TJ+JX=0$; tangent spaces elsewhere are its left translates.
= Tangent space of the symplectic group
At the identity, the symplectic Lie algebra consists of $X$ satisfying $X^TJ+JX=0$; tangent spaces elsewhere are its left translates.