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 explicitely $M$?

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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