On the little Weyl group of a real spherical space

Abstract In the present paper we further study of compression cone a real spherical homogeneous space $$Z=G/H$$ Z = G / H . particular provide geometric construction little Weyl group Z introduced recently by Knop and Krötz. Our technique is based on fine analysis limits conjugates subalgebra $$\mathrm{Lie}(H)$$ Lie ( ) along one-parameter subgroups in Grassmannian subspaces $$\mathrm{Lie}(G)$$ The obtained as finite reflection generated reflections walls cone.