Given a compact, connected, semisimple Lie group $G$ it is known that: \begin{equation} Z(G)=\Lambda_{weight}/\Lambda_{root} \end{equation} In this question there is an explanation of why this is true.
I would now like to construct the explicit map that given a certain weight associates to it an element of the center of the group. I thought of following the path of the question above, but I wasn't able to get anything.
Can someone provide me suggestions or show me a simple example of how this work?