Analogues of Weyl's Formula for Reduced Enveloping Algebras

Abstract

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.

Keywords:

• Weyl dimension formula
• reduced enveloping algebra
• affine Weyl group
• Kazhdan-Lusztig cells