Generalized Verma modules on a class of simple Lie algebras
Generalized Verma modules are the natural generalization of Verma modules.To get some new representations of simple Lie algebras,we discussed the irreducibility of the generalized Verma module of B2 induced from sl(2,C).The study started from the roots and the root vectors of the Lie algebra g of type B2.A group of bases of g was given.We used their Lie product relations,the triangular decomposition of g and the Whittaker module of sl(2,C)to induce the generalized Verma module.The irreducibility of the generalized Verma module is determined by discussing the generating vectors.
generalized Verma modulesimple moduleWhittaker moduleLie algebra of type B2
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