I am stuck on this problem and cannot seem to find a good reason for drawing the required conclusion. The problem is as follows:
I know that the maximal dimension of abelian Lie subalgebra of $Lie(Sp(2n,\mathbb{R})=C_n$: symplectic Lie algebra equal to $k:=\dfrac{n(n+1)}{2}$, is this mean that the maximal dimension of abelian subgroup of $Sp(2n,\mathbb{R})$ is $k$?
Any help would be much appreciated. Thanks!