Counting components of the null-cone on tuples

For a finite-dimensional representation of a group G, the diagonal action of G on p-tuples of elements of M, is usually poorly understood. The algorithm presented here computes a geometric characteristic of this action in the case where G is connected and reductive, and is a morphism of algebraic groups: The algorithm takes as input the weight system of M, and it returns the number of irreducible components of the null-cone of G on for large p. The paper concludes with a theorem that if the characteristic is zero and G is semisimple, then only few M have the property that is small for all p.