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Results tagged with symplectic-group
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user 297
6
votes
Zariski density of conjugates of $SL_2(\mathbb{Z})$ in $Sp_{2g}$
This seems impossible to me, at least with the kind of embedding considered or anything remotely close to it. I'll think classically, in terms of $\mathbb{C}$ points. Your embedding $SL_2(\mathbb{Z})$ …
- 156k
2
votes
Symplectic group over $\mathbb{Z}/p\mathbb{Z}$ is generated by its root subgroups
I'll spell out Andrei Smolensky's argument a bit (and remove this from the unanswered list).
(1) For any field $k$, the group $\operatorname{SL}_2(k)$ is generated by its elementary subgroups. In part …