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Irreducible modules of modular Lie superalgebras and super version of the first Kac–Weisfeiler conjecture
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 11 December 2023, pp. 554-573
- Print publication:
- September 2024
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- Article
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Suppose
$\mathfrak {g}=\mathfrak {g}_{\bar 0}+\mathfrak {g}_{\bar 1}$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field 
$\mathbf {k}$ of characteristic 
$p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra 
$U(\mathfrak {g})$ of 
$\mathfrak {g}$, 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.
