ABSTRACT
In this chapter we address the problem of constructing generators for F[K]G in some concrete way when V is a finite dimensional G-representation. Some of the ideas come from algebraic topology: the theory of characteristic classes of vector bundles, in particular the splitting principle. This leads to the notion of orbit polynomials and orbit Chern classes. It was motivated by an attempt to understand WeyPs account [259] (pp. 275-276) of E. Noether’s [170] proof of Hilbert’s finiteness theorem. In her paper [170] E. Noether gave two proofs of the existence of a finite system of algebra generators for W[V]G when G is a finite group and F a field of characteristic zero. We have already seen one of these, 2.4.2 in section 2.4. In this chapter we examine the second of these, which contains an algorithm for constructing a complete system of fundamental invariants. The basic references for this chapter are [170] and [221] .
