4 problems

Strong-generation conjecture. If $G$ is not $\operatorname{Spin}(2N)$, then $\mathbf{I}_G$ is strongly generated by $(P_i)_{i=1}^{\operatorname{rk}\mathfrak{g}}$ and generators…

Chiral generator conjecture. Suppose $G$ is not $\operatorname{Spin}(2N)$. Then $\mathbf{I}_G$ is isomorphic to the vertex subalgebra of $\Pi_G$ weakly generated by…

Poisson generation conjecture. If $G$ is not simply connected, or if $G$ is not of type $D_{2N}$, then $I_G$ is Poisson generated by $(P_i)_{i=1}^{\operatorname{rk}\mathfrak{g}}$ a…

Algebraic generator conjecture. If $G$ is not simply connected, or if $G$ is not of type $D_{2N}$, then $I_G$ is generated, as a ring, by the fundamental invariants…