Weyl-algebra subalgebra graph-admissibility conjecture

Let $A_n$ be the complex $n$-mode Weyl algebra, and let $\mathfrak{g}$ be a finite-dimensional Lie subalgebra of $A_n$. Weyl-algebra subalgebra conjecture. Every finite-dimensional Lie subalgebra of $A_n$ is graph-admissible but not necessarily minimal-graph-admissible. This asks whether graph-admissibility persists for finite-dimensional subalgebras in higher-mode Weyl algebras, while minimal graph-admissibility may fail.