Abstract
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.
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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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Presented by: Alistair Savage
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Holmes, R.R., Zhang, C. Simplicity of Kac Modules for the Quantum General Linear Superalgebra. Algebr Represent Theor 23, 1737–1760 (2020). https://doi.org/10.1007/s10468-019-09910-7
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DOI: https://doi.org/10.1007/s10468-019-09910-7
Keywords
- Quantum supergroup
- Quantum enveloping superalgebra
- General linear
- Representation
- Kac module
- Simple module