6 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…

Three-simple-module conjecture. The tensor product

Adjoint decomposition conjecture. The commutator action of ${\boldsymbol U}_{\star}$ on itself should decompose into irreducible representations in the same way as the adjoint acti…

Stable tensor-power decomposition conjecture. The decomposition of

Let $U(\mathfrak{o}(\infty))$ be the universal enveloping algebra of the infinite-dimensional orthogonal Lie algebra, and call a primitive ideal integrable when it arises from an i…