Panov, A. N. Irreducible representations of the Lie algebra \(sl(n)\) over a field of positive characteristic. (Russian) Zbl 0585.17009 Mat. Sb., N. Ser. 128(170), No. 1(9), 21-34 (1985). The author investigates the structure of irreducible representations of the Lie algebra \(sl(n)\) over an algebraically closed field of characteristic \(p>n\). Such representations can be extended to representations of the universal enveloping algebra mapping the elements of its center into scalar operators. Among these elements are those of the form \(x^ p-x^{[p]}\), and their representation as scalars under such a representation is called a \(p\)-character. Every irreducible representation with a given \(p\)-character is shown to be a quotient of a certain universal representation with that character, and equivalent conditions are given for such a representation to have maximal dimension. Reviewer: Gordon Brown (Boulder) Cited in 1 ReviewCited in 1 Document MSC: 17B50 Modular Lie (super)algebras 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) Keywords:prime characteristic; irreducible representations; special linear Lie algebra; universal enveloping algebra; \(p\)-character; universal representation; maximal dimension PDF BibTeX XML Cite \textit{A. N. Panov}, Mat. Sb., Nov. Ser. 128(170), No. 1(9), 21--34 (1985; Zbl 0585.17009) Full Text: EuDML