  Let $G_{\mathbb R}$ be the set of real points of a complex linear reductive
group and $\hat G_\lambda$ its classes of irreducible admissible
representations with infinitesimal integral regular character $\lambda$. In
this case each cell of representations is associated to a \emph{special}
nilpotent orbit. This helps organize the corresponding set of irreducible
Harish-Chandra modules. The goal of this paper is to is to describe algorithms
for identifying the special nilpotent orbit attached to a cell in terms of
descent sets appearing in the cell.
