The fantastic answers to my previous question [Subgroups of $SL\_2(\mathbb R)$ which contain $SL\_2(\mathbb Z)$ as a finite index subgroup](https://mathoverflow.net/q/252000) led me to the following question.


Let $O\_K$ be the ring of integers of $K= \mathbb{Q}(\sqrt{p})$, where $p$ is a prime number.


What are the subgroups $\Gamma \subset \mathrm{Sp}(2g,O\_K)$ of infinite index which contain $\mathrm{Sp}(2g,\mathbb Z)$? Are there any?



Subgroups of $Sp(2n,\mathbb{R})$ between $Sp(2n,\mathbb{Z})$ and some arithmetic group
First of all, thank you for the adjective "fantastic"(!). The question is actually studied in a paper of mine [(link to the MR review)](http://www.ams.org/mathscinet-getitem?mr=1324463). Sorry for talking about my own paper (I have no option, since I do not know if anyone else is interested enough in these questions). 


[I should add that, in all this, $g\geq 2$].
In the paper referred to above, what is proved is that any intermediate subgroup either has finite index in $Sp\_{2g}(O\_K)$ or else contains $Sp\_{2g}(\mathbb{Z})$ as a finite index subgroup. In particular, since $Sp\_{2g}(\mathbb{Z})$ is a maximal discrete subgroup of $Sp\_{2g}(\mathbb{R})$ by the answers to your previous question, there are no in-between subgroups of infinite index in $Sp\_{2g}(O\_K)$ other than $Sp\_{2g}(\mathbb{Z})$. 


