Verma modules and differential conformal invariants. (English) Zbl 0732.53011

From the author’s abstract: “A distinguished class of differential invariants of conformal structures is constructed using homomorphisms of Verma modules and Cartan’s conformal connection. This class reduces to a large subset of the class of differential operators invariant by conformal translation on flat conformal manifolds, and operators in it may be expressed in terms of the Levi-Civita connection and the Ricci curvature of a metric on the conformal class. Composition of these differential operators yields further differential invariants which depend on the conformal curvature.


53A30 Conformal differential geometry (MSC2010)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
58J70 Invariance and symmetry properties for PDEs on manifolds
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