Recursive algebraic construction of two infinite families of polynomials in
n variables is proposed as a uniform method applicable to every semisimple
Lie group of rank n. Its result recognizes Chebyshev polynomials of the first
and second kind as the special case of the simple group of type A1. The
obtained not Laurent-type polynomials are proved to be equivalent to the
partial cases of the Macdonald symmetric polynomials. Basic relation between
the polynomials and their properties follow from the corresponding properties
of the orbit functions, namely the orthogonality and discretization. Recurrence
relations are shown for the Lie groups of types A1, A2, A3, C2,
C3, G2, and B3 together with lowest polynomials.Comment: 34 pages, some minor changes were done, to appear in IJMM