On orthogonal and orthonormal characters

R”G (and RSG) on the one side, and R;G (and RiG) on the other side, are defined as subgroups of RG and R,G, respectively, having as generators the G-modules which admit an orthogonal (a symplectic), G-invariant bilinear form over the field C of complex numbers, respectively over K. RFG is the subgroup of R,G that is spanned by the G-modules which are equipped with an orthogonal, G-invariant bilinear form over K to which there exists an orthonormal K-basis. RYG then is the subgroup of R, G that is generated by the PZ 9 K, where wz itself possesses an orthogonal, G-invariant bilinear form over D to which there exists an orthonormal D-basis. The following diagram roughly shows how all these groups are correlated.