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.


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.)
Full Text: DOI Euclid


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