Abstract
The classical Rankin–Cohen brackets are bi-differential operators from \(C^\infty ({\mathbb {R}})\times C^\infty ({\mathbb {R}})\) into \( C^\infty ({\mathbb {R}})\). They are covariant for the (diagonal) action of \(\mathrm{SL}(2,{\mathbb {R}})\) through principal series representations. We construct generalizations of these operators, replacing \({\mathbb {R}}\) by \({\mathbb {R}}^n,\) the group \(\mathrm{SL}(2,{\mathbb {R}})\) by the group \(\mathrm{SO}_0(1,n+1)\) viewed as the conformal group of \({\mathbb {R}}^n,\) and functions by differential forms.
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S. Ben Saïd is thankful to UAEU for the Start-up Grant No. G00002950.
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Communicated by C. Schweigert
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Ben Saïd, S., Clerc, JL. & Koufany, K. Conformally Covariant Bi-differential Operators for Differential Forms. Commun. Math. Phys. 373, 739–761 (2020). https://doi.org/10.1007/s00220-019-03431-6
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DOI: https://doi.org/10.1007/s00220-019-03431-6