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Questions about the branch of algebra that deals with groups.

2 votes
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Finding invariant closed subspace which are also subgroups for the action of $\text{SL}(2, \...

I recently came across to the following action of $\text{SL}(2,\Bbb Z)$ on the space $\Bbb R^n\times\Bbb R^n$ defined as $$ \begin{pmatrix} a & b \\ c & d \end{pmatrix}\cdot \big(v,\,w\big)\mapsto \b …