Abstract
The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of some conformally invariant operators in the Rarita-Schwinger setting. We also study properties of some other Rarita-Schwinger type operators, for instance, twistor operators and dual twistor operators. This work is also intended as an attempt to motivate the study of Rarita-Schwinger operators via some representation theory. This calls for a review of earlier work by Stein and Weiss.
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Acknowledgements
The authors wish to thank the referee for helpful suggestions that improved the manuscript. The authors are also grateful to Bent Ørsted for communications pointing out that the intertwining operators for the Rarita-Schwinger operators are special cases of Knapp-Stein intertwining operators in higher spin theory [5, 12].
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Ding, C., Ryan, J. (2018). On Some Conformally Invariant Operators in Euclidean Space. In: Cerejeiras, P., Nolder, C., Ryan, J., Vanegas Espinoza, C. (eds) Clifford Analysis and Related Topics. CART 2014. Springer Proceedings in Mathematics & Statistics, vol 260. Springer, Cham. https://doi.org/10.1007/978-3-030-00049-3_4
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