Experimental Mathematics

Analogues of Weyl's Formula for Reduced Enveloping Algebras

J. E. Humphreys

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Abstract

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.

Article information

Source
Experiment. Math., Volume 11, Issue 4 (2002), 567-573.

Dates
First available in Project Euclid: 10 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1057864665

Mathematical Reviews number (MathSciNet)
MR1969647

Zentralblatt MATH identifier
1162.17302

Subjects
Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 17B45: Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 17B50: Modular Lie (super)algebras 20G05: Representation theory

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

Citation

Humphreys, J. E. Analogues of Weyl's Formula for Reduced Enveloping Algebras. Experiment. Math. 11 (2002), no. 4, 567--573. https://projecteuclid.org/euclid.em/1057864665


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