Sign signatures and characters of Weyl Groups

Let GR be the set of real points of a complex linear reductive group and Gˆλ, its classes of irreducible admissible representations with infinitesimal integral regular character λ. In this case, each cell of representations is associated to a special nilpotent orbit. This helps organize the corresponding set of irreducible Harish-Chandra modules. The goal of this paper is to bypass the need for the character table of the Weyl group associated with Gˆλ in the Springer correspondence, by describing a new and less computationally intensive parametrization of irreducible representations of simple complex Weyl groups.