Abstract
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials. These differential operators are symmetry breaking for the pair of Lie groups \((SL(2, \mathbb{C}),SL(2, \mathbb{R}))\) that arise from conformal geometry.
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Acknowledgements
The first author warmly thanks Professor Vladimir Dobrev for his hospitality during the tenth International Workshop: Lie Theory and its Applications in Physics in Varna, Bulgaria, 17–23 June 2013. Authors were partially supported by CNRS, the FMSP program at the Graduate School of Mathematical Sciences of the University of Tokyo, and Japan Society for the Promotion of Sciences through Grant-in-Aid for Scientific Research (A) (25247006) and Short-Term Fellowship (S13024).
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Kobayashi, T., Kubo, T., Pevzner, M. (2014). Vector-Valued Covariant Differential Operators for the Möbius Transformation. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_6
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DOI: https://doi.org/10.1007/978-4-431-55285-7_6
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