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Do these Zariski-dense subgroups of complex Chevalley group have non-empty intersection with this Bruhat cell?
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Do these Zariski-dense subgroups of complex Chevalley group have non-empty intersection with this Bruhat cell?
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Do these Zariski-dense subgroups of complex Chevalley group have non-empty intersection with this Bruhat cell?
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Do these Zariski-dense subgroups of complex Chevalley group have non-empty intersection with this Bruhat cell?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
@YCor Thank you yes I did miss this simple fact as Misha pointed, in regards to the second question I believe that $Be_{1,1}B$ is a Bruhat cell (which is not the big cell)
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Do these Zariski-dense subgroups of $\operatorname{SO}_{6}(\mathbb C)$ have non-empty intersection with this subset?
I use the definition $\operatorname{SO}_{2n}(k)=\{A\in\operatorname{GL}_{2n}(k)|A^TJ_{2n}A=J_{2n}\}$ where $J_{2n}$ is the identity matrix flipped 90 degrees