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Group representations arising from Lorentz conformal geometry. (English) Zbl 0643.58036
Author’s abstract: “It is shown that there exist conformally covariant differential operators \(D_{2\ell,k}\) of all even orders \(2\ell\), on differential forms of all orders k, in the double cover \(M^ n\) of the n-dimensional compactified Minkowski space \(M^ n\). These act as intertwining differential operators for natural representations of \(O(2,n)\), the conformal group of \(M^ n\). For even n, the resulting decompositions of differential form representations of \(O^{\uparrow}(2,n)\), the orthochronous conformal group, produce infinite families of unitary representations, the most interesting of which are carried by “positive mass-squared, positive frequency” quotients for \(2\ell \geq | n-2k|\).”
Reviewer: S.Eloshvili

MSC:
58J90 Applications of PDEs on manifolds
53C80 Applications of global differential geometry to the sciences
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