Finite Generation of Invariants
Larry Smith · 1995
Chapter 2 Finite Generation of Invariants For a finite group G, a field of coefficients W and a finite dimensional repre sentation q : G GL(V&s;), there is the action of G on the ring of polynomial functions W[V] via (gf)(v) = f(g(g~1)v), and the ring of invariants JF[V]G. A problem of basic importance is the finiteness problem: does there exist (as in the case of the tautological representation of the symmetric group and the alternating group) a finite set of polynomials f \, . . . , f s (called fundamental integral invariants or a complete fundamental system of invariants in the 19th century) such that every invariant polynomial f e JF[V]g can be expressed as a polynomial in / i , . . . , f s?