Analogues of Weyl's formula for reduced enveloping algebras

Details Analogues of Weyl's formula for reduced enveloping algebras Analogues of Weyl's formula for reduced enveloping algebras

2002-07-22

arxiv.org/abs/math/0207195v1

Experiment. Math. 11 (2002), no. 4, 567--573 (2003)

Mathematics

Representation Theory

AMS-LaTeX, 10 pages, 2 figures

Scientific paper

In this note we study simple modules for a reduced enveloping algebra
U_chi(g) in the critical case when chi element of 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.

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