# Levi subgroup of Siegel parabolic of GSpin

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.

• I think that if you indeed want to get an answer, you should make an effort to explain clearly what you are asking.... – Mikhail Borovoi Mar 8 '19 at 0:57

The Levi part would be $$GL(n)\times GL(1)$$. By the way, the Siegel parabloic is not unique in the even rank case.