  A covariant hyper-nuclear energy density functional (EDF) is derived from in
medium nucleon meson vertex functionals, assuring the proper description of
nuclear mean-field dynamics. The fundamental SU(3) coupling constants for the
mean-field relevant vector (m=V) and scalar (m=S) interactions as functionals
of the total baryon density are determined. Scalar and vector potentials and
the resulting hyperon mean-fields in asymmetric nuclear matter are constructed
and discussed, addressing also effects from three-body interactions. \Lambda-
\Sigma^0 mixing in asymmetric nuclear through the coupling to the background
isovector mean-field is addressed.
