Analogues of Weyl's Formula for Reduced Enveloping Algebras

In this paper, we study simple modules for a reduced enveloping algebra U x (g) in the critical case when X ∈ g* 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.