Irreducible modules of modular Lie superalgebras and super version of the first Kac-Weisfeiler conjecture
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES（2023）
摘要
Suppose g = g(0)+g(1) is a finite-dimensional restricted Lie superalgebra over an algebraically closed field k of characteristic p > 2. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra U(g) of g, as a super generalization of the celebrated first Kac-Weisfeiler conjecture. It is demonstrated that the conjecture holds for all basic classical Lie superalgebras and all completely solvable restricted Lie superalgebras. In this process, we investigate irreducible representations of solvable Lie superalgebras.
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关键词
Modular Lie superalgebras,maximal dimensions of irreducible modules,the first Kac-Weisfeiler conjecture
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