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Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in two cases, namely, the 3 system for type A2 and type D4. Here, such a system is shown to exist for both cases. The construction of the system may also be interpreted as giving an explicit homomorphism between generalized Verma modules.

A system of third-order differential operators conformally invariant under sl(3,ℂ) and so(8,ℂ)