Index of parabolic and seaweed subalgebras of

The index of a Lie algebra is defined as , where is the stabilizer of w under the coadjoint action of on . In this paper we derive simple formulas for the index of parabolic subalgebras of the even orthogonal algebra . We use these formulas to prove the conjecture that for any parabolic subalgebra or seaweed subalgebra (intersection of two weakly opposite parabolics) of . Some partial results for subalgebras of are also obtained.