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Jul 3, 2023 at 16:57 comment added Stefan Dawydiak Note also that when $G$ is not connected, the various connected components of $\mathrm{Spec}(R(G))$ have different dimensions in general. See for example the case of even orthogonal groups in H. Minami, "THE REPRESENTATION RINGS OF ORTHOGONAL GROUPS" Osaka J. Math. (8) 1971, 243–250.
Jun 30, 2023 at 10:06 comment added abx If $G$ is connected, $R(G)=R(T)^W$, where $T$ is a maximal torus and $W$ the Weyl group. Then $\dim R(G)=\dim R(T)^W=\dim R(T)= \operatorname{rk}G+1 $.
S Jun 30, 2023 at 9:37 review First questions
Jun 30, 2023 at 9:38
S Jun 30, 2023 at 9:37 history asked Markuss Schmuckler CC BY-SA 4.0