CONJUGACY AND ELEMENT-CONJUGACY OF HOMOMORPHISMS OF COMPACT LIE GROUPS

Let G be a connected compact Lie group. Among other things, we prove that the following are equivalent. (a) For all connected compact Lie groups H and all continuous homomorphisms phi, phi' V H -> G, if phi(h) and phi'(h) are conjugate in G for all h epsilon H, then phi and phi' are G-conjugate. (b) The Lie algebra of G contains no simple ideal of type D-n (n >= 4), E-6, E-7, or E-8.