The following orthogonal groups claimed to have the isomorphism (see the Abstract of this paper or here PDF) to Symplectic group:
$$O(2,1) \simeq Sp(2;\mathbb{R})?$$ $$O(3,1) \simeq Sp(2;\mathbb{C})?$$ $$O(4,1) \simeq Sp(2;\mathbb{H})?$$
See also PDF
How to justify or falsify these isomorphisms?
Do we have other isomorphisms?
$$O(d,1) \simeq Sp(n;\mathbb{F})?$$
for other $d$, $n$ and $\mathbb{F}$? or other than $Sp$?
Can we show these isomorphisms (by wise arguments, no need to be sophisticated proofs)?
(p.s. We also know that $Spin(3,1) \simeq SL(2;\mathbb{C})$.)
Many Thanks!