Abstract :
The equivariant ordered K0-theory of the infinite tenser product of a fixed finite dimensional representation of a compact connected Lie group is shown to reduce to that of the maximal torus, for almost all (but not all) choices of representation. Specifically, for almost any character χ and generalized character ψ there exists a power of χ so that the product χn ψ is a character if and only if a similar product of their restrictions to a maximal torus is a character of the torus. If χ is irreducible and this property fails for some ψ, then the highest weight of χ lies on the boundary of the Weyl chamber.
