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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.

MSC:

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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