Equivariant bifurcation theory and symmetry breaking

A study is made of the failure of the Maximal Isotropy Subgroup Conjecture for the Weyl group seriesW(D) _k . As part of the investigation, a general genericity and stability theorem is proved for bifurcation diagrams in equivariant bifurcation theory. As well, a concept of determinacy for equivariant bifurcation theory is introduced and it is shown that, for all compact Lie groupsG and absolutely irreducibleG-representationsV, G-equivariant bifurcation problems onV are finitely determined.