The existence of a polynomial factorization map for some compact linear   groups
  It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected components, and its representation should be the direct sum of three irreducible two-dimensional real representations at least two of them being faithful. 
O. G. Styrt
math.AG math.DG