Weyl Group Characters Afforded By Zero Weight Spaces

Let G be a compact Lie group with Weyl W. We give formula for the character of W on zero weight space any finite-dimensional representation G. The involves weighted partition functions, generalizing Kostant’s function. On elliptic set W, functions are trivial. regular set, is monomial product certain coroots, up to constant equal 0 or ± 1. This generalizes trace Coxeter element space. If long w0 = ? 1, our gives method determining all representations which irreducible.