Geometric properties of homogeneous parabolic geometries with   generalized symmetries
  We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic geometries, we prove that the reductions correspond to known generalizations of symmetric spaces. In addition, we illustrate our results on an explicit example and provide a complete classification of possible non--trivial cases. 
Jan Gregorovi\v{c} and Lenka Zalabov\'a
math.DG