Representations whose minimal reduction has a toric identity component
  We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the non-polar irreducible representations preserving an isoparametric submanifold and acting with cohomogeneity one on it. 
Claudio Gorodski and Alexander Lytchak
math.DG math.MG math.RT