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Invariants of conformal densities. (English) Zbl 0745.53007
In this paper scalar invariants of conformal densities are studied on the sphere with its conformally flat structure. A density of weight \(w\in \mathbb{C}\) on a smooth manifold \(M^ n\) is a section of the line bundle \(| \Lambda^ nT^*M|^{-w/n}\). A construction of these scalar invariants is given. If neither \(w+n/2\) nor \(w+1\) is a positive integer, then it is shown that all invariants arise by this construction. The relationship between certain problems of parabolic invariant theory and the theory of generalized Verma modules is explained.

MSC:
53A30 Conformal differential geometry (MSC2010)
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
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