On the homomorphisms between the generalized Verma modules arising from conformally invariant systems (Q2856392)

The generalized Verma modules studied in this paper are modules over semi-simple Lie algebras which are induced by a finite-dimensional simple module over a parabolic subalgebra. Unlike the classical Verma modules, the dimension of homomorphism space between such generalized Verma modules can be bigger than one and not all non-zero homomorphisms between such generalized Verma modules are injective. A standard homomorphism between generalized Verma modules is the one induced from a non-zero homomorphism between the corresponding Verma modules. Some homomorphisms between generalized Verma modules arise from certain conformally invariant systems of differential operators. The author determines when homomorphisms arising from conformally invariant systems of first- and second-order differential operators are standard.