  Polynomials in this paper are defined starting from a compact semisimple Lie
group. A known classification of maximal, semisimple subgroups of simple Lie
groups is used to select the cases to be considered here. A general method is
presented and all the cases of rank not greater then 3 are explicitly studied.
We derive the polynomials of simple Lie groups B_3 and C_3 as they are not
available elsewhere. The results point to far reaching Lie theoretical
connections to the theory of multivariable orthogonal polynomials.
