1 S ep 2 00 6 On conformally invariant differential operators .
نویسنده
چکیده
We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the dimension. The method relies only on a study of wellknown transformation laws and on the formalism of Weyl about identities holding “formally” vs. “by substitution”. We also illustrate how this new method can strengthen existing results in the parabolic invariant theory for conformal geometries.
منابع مشابه
56 v 1 2 7 O ct 2 00 4 Description of all conformally invariant differential operators , acting on scalar functions
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متن کاملar X iv : m at h / 06 08 77 1 v 1 [ m at h . D G ] 3 1 A ug 2 00 6 On conformally invariant differential operators
We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the dimension. The method relies only on a study of wellknown transformation laws and on the formalism of Weyl about identities holding “formally” vs. “by substitution”....
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We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the dimension. The method relies on a study of well-known transformation laws and on Weyl’s theory regarding identities holding “formally” vs. “by substitution”. We also...
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We give an algorithm write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent invariant operators of order up to k. The independent differential operators of second order are three and we give an explicit realization of them. The applied ...
متن کاملConformally invariant differential operators on tensor densities
Let Fλ be the space of tensor densities on R n of degree λ (or, equivalently, of conformal densities of degree −λn) considered as a module over the Lie algebra o(p+1, q+1). We classify o(p+1, q+1)-invariant bilinear differential operators from Fλ ⊗ Fμ to Fν . The classification of linear o(p + 1, q + 1)invariant differential operators from Fλ to Fμ already known in the literature (see [6, 9]) i...
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تاریخ انتشار 2008