An explicit construction of Casimir operators and eigenvalues. II

We provide a way of computing Casimir eigenvalues for Weyl orbits as well as for irreducible representations of Lie algebras. A κ(s) number of polynomials of rank N are obtained explicitly for A_N Casimir operators of order s where κ(s) is the number of partitions of s into positive integers except 1. It is also emphasized that these eigenvalue polynomials prove useful in obtaining formulas to calculate weight multiplicities and in explicit calculations of the whole cohomology ring of classical and also exceptional Lie algebras.