Intrinsic construction of invariant functions on simple Lie algebras

An algorithm for constructing primitive adjoint-invariant functions on a complex simple Lie algebra is presented. The construction is intrinsic in the sense that it does not resort to any representation. A primitive invariant function on the whole Lie algebra is obtained by lifting a coordinate function on a Kostant slice of the Lie algebra. Such an intrinsic construction of invariant functions is most useful for the bigger exceptional Lie algebras such as the E's. The Maple implementation of this algorithm is outlined at the end and will be applied to these exceptional Lie algebras in a future work.