Modular representations of simple Lie algebras

Author:

Humphreys J.

Abstract

In spite of many efforts over the past 50 years, the irreducible representations of the Lie algebra of a simple algebraic group over a field of prime characteristic are poorly understood. Recent work on quantum groups at a root of unity has provided new impetus for the subject. This article surveys what has been done and what remains to be done.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference81 articles.

1. The irreducible characters for semi-simple algebraic groups and for quantum groups;Andersen, Henning Haahr,1995

2. Representations of quantum groups at a 𝑝th root of unity and of semisimple groups in characteristic 𝑝: independence of 𝑝;Andersen, H. H.;Ast\'{e}risque,1994

3. Representations of rank one Lie algebras of characteristic 𝑝;Benkart, Georgia M.,1982

4. The 𝑢-algebra of a restricted Lie algebra is Frobenius;Berkson, Astrid J.;Proc. Amer. Math. Soc.,1964

5. Representations of modular Lie algebras through quantum groups;Chari, Vyjayanthi;C. R. Acad. Sci. Paris S\'{e}r. I Math.,1993

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