Structure of modules induced from simple modules with minimal annihilator

[摘要] We study the structure of generalized Verma modules over asemi-simple complex finite-dimensional Lie algebra, which areinduced from simple modules over a parabolic subalgebra. We considerthe case when the annihilator of the starting simple module is aminimal primitive ideal if we restrict this module to the Levi factor ofthe parabolic subalgebra. We show that these modules correspond toproper standard modules in some parabolic generalization of theBernstein-Gelfand-Gelfand category $Oo$ and prove that the blocks ofthis parabolic category are equivalent to certain blocks of thecategory of Harish-Chandra bimodules. From this we derive, inparticular, an irreducibility criterion for generalized Verma modules.We also compute the composition multiplicities of those simplesubquotients, which correspond to the induction from simple moduleswhose annihilators are minimal primitive ideals.

[学科分类] 数学（综合）