Does anybody know why the quotient of $SL_n$ by its subgroup $Q_m:=\left\{\left(\begin{matrix}\xi&*&\cdots&*\\0&*&\cdots&*\\ \vdots&\vdots&\ddots&\vdots\\ 0&*&\cdots&*\end{matrix}\right)\mid\xi\in\mu_m\right\}$ is isomorphic to $\mathbb{C}^n/\mu_m$, where $\mu_m$ is the cyclic group of order $m$ and acts diagonally on $\mathbb{C}^n$?
2026-03-26 03:11:35.1774494695
quotient of SL_n
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