Let G be a compact Lie group with a maximal torus T, then what does the complex representation of G $\alpha:G\rightarrow U(n)$ mean? Does it mean that regarding $\alpha(g)$ as an isometry on $C^n$ for $g\in G$?

Also, it will be good someone let me know the representations $\alpha:G\rightarrow U(n)$ for $G=G_2,F_4,E_6,E_7,E_8$? I don't have J.F.Adams's book "Lectures on exceptional lie groups"at hand.