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I consider the group $G=\mathrm{GSpin(V)}$ as in this question.

We have the so called Siegel parabolic $P$ (after fixing a cocharacter) and the associated Levi $M$ (these can also be obtained using the corresponding objects in $\mathrm{GSp}$).

Can we describe explicitly $M$?

I think it is isomorphic to some product of $\mathrm{GL}_i$, but I am not sure.

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    $\begingroup$ I think that if you indeed want to get an answer, you should make an effort to explain clearly what you are asking.... $\endgroup$ – Mikhail Borovoi Mar 8 '19 at 0:57
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The Levi part would be $GL(n)\times GL(1)$. By the way, the Siegel parabloic is not unique in the even rank case.

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  • $\begingroup$ Could you explain why this is the Levi part? $\endgroup$ – Michael Albanese Aug 13 at 10:52

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