11 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…

Pirashvili's conjecture. A perfect complex Lie algebra is semisimple if and only if

Finite generation conjecture. The VOSA $H(W^{\infty /2}\tilde{\ell},Q)$ is finitely generated for semisimple $\ell$.

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 and let $\mathfrak{S}$ be a Lie ring. A map $\beta\colon\mathfrak{g}\to\mathfrak{S}$ is commutator-preserving if it preserves the Lie…

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 Lie algebra, and let $HL_p(\mathfrak{g},K)$ denote its Leibniz homology with trivial coefficients. Pirashvili's weak conjecture. The Lie algebra…

Let $\mathfrak{g}$ be a semisimple Lie algebra over a field of characteristic $p$, let $e\in\mathfrak{g}^*$ be nilpotent, and let $d(e)$ be the codimension of the Springer fiber…

Let $\mathfrak{g}$ be a semisimple Lie algebra with Weyl group $W$, let $\overline{\mathfrak{g}}$ be the ambient semisimple Lie algebra with dominant weights $\overline{P}_{+}$ and…

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…