2 problems

Let $\mathfrak{so}(N)$ be the orthogonal Lie algebra, and let $\operatorname{ad}$ denote its adjoint representation. For a Young diagram $\lambda$, write $\lambda\vdash 2m$ when it…

Let $\fg$ be an orthogonal Lie algebra of type $B$ or $D$, of rank $n$, and write a Levi subalgebra as … with $b_1\geqslant\cdots\geqslant b_k\geqslant1$. Let…