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Sep 12, 2021 at 9:07 vote accept Puzzled
Mar 8, 2020 at 10:21 comment added Puzzled Thank you very much to you all for the answer and the comments. I modified my question to better explain what is confusing me about the irreducibility of the symplectic group.
Mar 7, 2020 at 10:37 comment added YCor PS: connectedness still holds for the stabilizer of an arbitrary alternating form: indeed it has a matrix block-triangular decomposition with diagonal blocks $\mathrm{Sp}(2n)$ and $\mathrm{GL}_m$, and upper block abelian unipotent of dimension $2mn$ (the unipotent radical).
Mar 7, 2020 at 8:54 history answered YCor CC BY-SA 4.0