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Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type. (English) Zbl 1277.22013

Let \(G_0\) be a simple Lie group and \(Q_0\) a maximal parabolic subgroup of quasi-Heisenberg type. The author constructs conformally invariant systems of differential operators associated to a homogeneous line bundle \(\mathcal{L}_s\longrightarrow G_0/Q_0\). These systems yield explicit homomorphisms between appropriate generalized Verma modules. Furthermore, it is determined whether these homomorphisms are standard or not.

MSC:

22E46 Semisimple Lie groups and their representations
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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References:

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