Isomorphism between Systems of Equivariant SingularitiesU

In this article isomorphisms between systems of singularities equivariant under different Lie group actions are investigated and a sufficient condition for two systems to be isomorphic is given. With this sufficiency theorem we show that the system of O n.-equivariant singularities in its irreducible representation on Rn is isomorphic to that of one-dimensional Z2-equivariant singularities and the system of 1n nq1.-dimensional O n.-equivariant singularities is isomorphic to that of 2 n-dimensional Sn-equivariant singularities