6 problems

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with weight lattice notation $P^+$, and let $\rho$ be the half-sum of its positive roots. For a dominant integral weight…

Let $\mathfrak{g}$ be a finite-dimensional graph-admissible Lie algebra associated with the labeled directed graph $G(V,E)$. Graph semisimplicity conjecture. The Lie algebra…

Let $\mathfrak g$ be a semisimple Lie algebra, let $f\in\mathfrak g$ be a non-zero nilpotent element, and let $\mathfrak s$ be an $\mathfrak{sl}_2$-triple containing $f$. A reducin…

Let $\mathfrak h$ be a real semisimple Lie algebra and $V$ an orthogonal representation of $\mathfrak h$. AGS conjecture. If $V$ has AGS in $\mathfrak h$, then … The conjecture giv…

Let $\mathfrak{g}$ be a non-trivial finite-dimensional complex Lie algebra. Say that $\mathfrak{g}$ satisfies the Pirashvili conditions if, equivalently, $HL_p(\mathfrak{g})=0$ for…

Let $\mathfrak{g}$ be a semisimple Lie algebra and let $V(\lambda)$ be an irreducible $\mathfrak{g}$-module of dimension $r$, with highest weight $\lambda$. Let $\Pi(\lambda)$ deno…