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Irreducible representations of the Lie algebra \(sl(n)\) over a field of positive characteristic. (Russian) Zbl 0585.17009
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.

17B50 Modular Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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