Generalized Verma Modules Induced from sl(2, ) and Associated Verma Modules

With each generalized Verma module induced from a “well-embedded” parabolic subalgebra of a Lie algebra with triangular decomposition, we associate a Verma module over the same algebra in a natural way. In the case when the semisimple part of the Levi factor of the parabolic subalgebra is isomorphic to sl(2, ) and the generalized Verma module is induced from an infinite-dimensional simple module, we prove that the associated Verma module is simple if and only if the original generalized Verma module is simple.