Simplicity of Kac Modules for the Quantum General Linear Superalgebra

  • Randall R. HolmesEmail author
  • Chaowen Zhang


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.


Quantum 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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  2. 2.Department of MathematicsChina University of Mining and TechnologyXuzhouPeople’s Republic of China

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