  Given a connected simply connected semisimple group G and a connected
spherical subgroup K we determine the generators of the extended weight monoid
of G/K, based on the homogeneous spherical datum of G/K.
  Let H be a reductive subgroup of G and let P be a parabolic subgroup of H for
which G/P is spherical. A triple (G,H,P) with this property is called
multiplicity free system and we determine the generators of the extended weight
monoid of G/P explicitly in the cases where (G,H) is strictly indecomposable.
  The extended weight monoid of G/P describes the induction from H to G of an
irreducible H-representation V whose lowest weight is a character of P. The
space of regular End(V)-valued functions on G that satisfy F(hgk)=hF(g)k for
all h,k in H and all g in G, is a module over the algebra of H-biinvariant
regular functions on G. We show that under a mild assumption this module is
freely and finitely generated. As a consequence the spherical functions of such
a type V can be described as a family of matrix-valued orthogonal polynomials.
