Timeline for Normalizers of subsystem subgroups of Lie groups

6 events

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Dec 20, 2018 at 16:00	comment	added	Victor Petrov		$D_6\times A_1$ seems to be self-normalizing, because it is the centralizer of $\mu_2$, the center of $A_1$ (for any $g$ normalizing $D_6\times A_1$ leaves $A_1$ invariant and therefore commutes with the center of $A_1$).
Dec 18, 2018 at 19:04	comment	added	Jim Humphreys		As you say, "My feeling is that this must be known, but I could not find anything." It may be "known" to someone, but it doesn't seem to be written down.
Dec 18, 2018 at 16:28	comment	added	Mikko Korhonen		What you are asking for is equivalent to computing the normalizer of the Weyl group of $H$ in the Weyl group of $G$. For this computation in the Weyl group, see Proposition 28 in Carter, "Conjugacy classes in the Weyl group" (1972). Looking at Table 10 in Carter's paper, you see that $D_6 \times A_1$ is self-normalizing in $E_7$. Another relevant reference is Howlett, "Normalizers of parabolic subgroups of reflection groups" (1980).
Dec 18, 2018 at 15:29	history	edited	Columbus1	CC BY-SA 4.0	added 5 characters in body
Dec 18, 2018 at 13:40	review	First posts
Dec 18, 2018 at 13:53
Dec 18, 2018 at 13:35	history	asked	Columbus1	CC BY-SA 4.0