Where can one find a table of generator–relator expressions for representation rings $R(G)$ of simple Lie groups $G$ and explicit maps between them? For example, given a maximal torus $T < G$ or a cover $\tilde G \to G$, I'd like this hypothetical table to have descriptions of the induced $$R(G) \rightarrowtail R(T),$$ $$R(G) \to R(\tilde G)$$ in terms of where they take generators. In principle, one could do this for oneself, but surely it's already written down somewhere.

**edit**: I'm aware that $R(T)$ is a Laurent polynomial ring, that $R(G) \cong R(T)^W$, and that $R(G)$ is a polynomial ring if $\pi_1 G$ is torsion-free or $G = \mathrm{SO}(2n+1)$, know what this implies for simply-connected classical groups, and know references to papers giving expressions for simply-connected exceptional groups. What I'm interested in is explicit descriptions for non–simply-connected groups in terms of their maximal tori and indications of where generators go under homomorphisms (including covering maps).