Let $G$ a semisimple group over an algebraically closed field $k$. We assume that $G$ is classical.
We call a $z$-extension, a group $\tilde{G}$ such that $\tilde{G}$ is a central extension of $G$ by a torus $Z$ and such that his derived group is simply connected.
Can we find a $z$-extension $\tilde{G}$ of $G$ such that it admits minuscule weights?
$G$
automaticaly lift to an extension group; so it's unclear what the problem is. $\endgroup$$A_\ell, D_\ell$
for instance). And the exceptional types$E_6, E_7$
do have minuscule weights. What is your source? $\endgroup$