ITERATED MULTIPLICATION OF CHARACTERS OF COMPACT CONNECTED LIE-GROUPS

The equivariant ordered K-0-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 chi and generalized character psi there exists a power of chi so that the product chi(n) psi is a character if and only if a similar product of their restrictions to a maximal torus is a character of the torus. If chi is irreducible and this property fails for some psi, then the highest weight of chi lies on the boundary of the Weyl chamber. (C) 1995 Academic Press, Inc.