This analysis establishes a relationship between generalized verma modules and tensor modules, highlighting their simplicity criteria.
A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules and tensor modules are established.
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Xue et al. (2025) studied this question.
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