Weyl Orbit Characters and Schur Functions

Abstract

For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations . For AN Lie algebras, weight multiplicities can then be calculated by only stating that charactres are equivalent to Schur functions. This also means that to calculate characters there is no need tos um over Weyl groupe . The compatibility with the Weyl character formula will however be shown.