In this paper, we study simple modules for a reduced enveloping algebra $\uxg$ in the critical case when $\chi \in \frg^*$ is "nilpotent.'' Some dimension formulas computed by Jantzen suggest modified versions of Weyl's dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan--Lusztig cells.
"Analogues of Weyl's Formula for Reduced Enveloping Algebras." Experiment. Math. 11 (4) 567 - 573, 2002.