Conformally Covariant Bi-differential Operators on a Simple Real Jordan Algebra

Abstract For a simple real Jordan algebra V, a family of bi-differential operators from $\mathcal{C}^\infty (V\times V)$ to $\mathcal{C}^\infty (V)$ is constructed. These operators are covariant under the rational action of the conformal group of V. They generalize the classical Rankin–Cohen bracket...

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Bibliographic Details
Published in:International mathematics research notices 2020-04, Vol.2020 (8), p.2287-2351
Main Authors: Ben Saïd, Salem, Clerc, Jean-Louis, Koufany, Khalid
Format: Article
Language:English
Subjects:
Differential Geometry
Mathematics
Representation Theory
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Summary:Abstract For a simple real Jordan algebra V, a family of bi-differential operators from $\mathcal{C}^\infty (V\times V)$ to $\mathcal{C}^\infty (V)$ is constructed. These operators are covariant under the rational action of the conformal group of V. They generalize the classical Rankin–Cohen brackets (case $V=\mathbb{R}$).
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rny082