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Let $G$ be an algebraic group over an algebraically closed field. Let $P$ be a standard parabolic subgroup of $G$ and $L$ be it's Levi subgroup. Do we have that weyl group of P equals weyl group of L? For Borel subgroup, it's seems true. Thank you very much.

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  • $\begingroup$ What is the definition of the Weyl group of such a parabolic subgroup? $\endgroup$ May 13, 2020 at 0:43
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    $\begingroup$ @Torsten Schoeneberg By Weyl group of $P$, we mean here $N_{P}(T) /T$ where $T$ is a common maximal torus for $P$ and $L$. $\endgroup$
    – user567863
    May 13, 2020 at 0:52

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