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This paper constructs a series of modules from modular Lie superalgebras W(0∣n), S(0∣n), and K(n) over a field of prime characteristic p≠2. Cartan subalgebras, maximal vectors of these modular Lie superalgebras, can be solved. With certain properties of the positive root vectors, we obtain that the sufficient conditions of these modules are irreducible L-modules, where L=W(0∣n), S(0∣n), and K(n)

advances in mathematical physics

Simple Modules for Modular Lie Superalgebras<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>∣</mml:mo></mml:mrow><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>S</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mrow><mml:mo>∣</mml:mo></mml:mrow><mml:mi>n</mml:mi><mml:mo stretchy="…

Simple Modules for Modular Lie SuperalgebrasW(0∣n),S(0∣n