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

AbstractWith 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,C) 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