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Analogues of Weyl’s formula for reduced enveloping algebras. (English) Zbl 1162.17302

Summary: In this paper, we study simple modules for a reduced enveloping algebra \(U_\chi(\mathfrak g)\) in the critical case when \(\chi\in\mathfrak g^*\) 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.

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B35 Universal enveloping (super)algebras
17B45 Lie algebras of linear algebraic groups
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