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For which semisimple element $s$ in finite group of lie type centralizer $C_{G}(s)$ of $s$ is a Levi subgroup ? |
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For which semisimple element $s$ in finite group of lie type $C_{G}(s)$ is a Levi subgroup ?Let $G$ be a finite simple group of lie type. Let $s$ be a semisimple element lying in maximal torus $T_{w}$ for $w\in W$ where $W$ is the Weyl group of $G$. Can we say that $C_{G}(s)$ is Levi subgroup of a Parobolic containing $s$ by looking just conjugacy class of $w$? I assume that $G'$ is simply connected.
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