Simplicity of Kac Modules for the Quantum General Linear Superalgebra
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A general necessary and sufficient condition is obtained for a Kac module of the quantum general linear superalgebra to be simple. More explicit conditions are then obtained by considering separately the case where the quantum parameter is not a root of unity and the case where it is a root of unity.
KeywordsQuantum supergroup Quantum enveloping superalgebra General linear Representation Kac module Simple module
Mathematics Subject Classification (2010)17B37 17B50
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The authors thank the referee for a careful reading of the paper and for several useful suggestions.
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