Conformally Covariant Bi-differential Operators for Differential Forms

Salem Ben Saïd; Jean Louis Clerc; Khalid Koufany

doi:10.1007/s00220-019-03431-6

Conformally Covariant Bi-differential Operators for Differential Forms

Salem Ben Saïd
, Jean Louis Clerc
, Khalid Koufany

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The classical Rankin–Cohen brackets are bi-differential operators from C^∞(R) × C^∞(R) into C^∞(R). They are covariant for the (diagonal) action of SL (2 , R) through principal series representations. We construct generalizations of these operators, replacing R by Rⁿ, the group SL (2 , R) by the group SO (1 , n+ 1) viewed as the conformal group of Rⁿ, and functions by differential forms.

Original language	English
Pages (from-to)	739-761
Number of pages	23
Journal	Communications in Mathematical Physics
Volume	373
Issue number	2
DOIs	https://doi.org/10.1007/s00220-019-03431-6
Publication status	Published - Jan 1 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "The classical Rankin–Cohen brackets are bi-differential operators from C∞(R) × C∞(R) into C∞(R). They are covariant for the (diagonal) action of SL (2 , R) through principal series representations. We construct generalizations of these operators, replacing R by Rn, the group SL (2 , R) by the group SO (1 , n+ 1) viewed as the conformal group of Rn, and functions by differential forms.",

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AB - The classical Rankin–Cohen brackets are bi-differential operators from C∞(R) × C∞(R) into C∞(R). They are covariant for the (diagonal) action of SL (2 , R) through principal series representations. We construct generalizations of these operators, replacing R by Rn, the group SL (2 , R) by the group SO (1 , n+ 1) viewed as the conformal group of Rn, and functions by differential forms.

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JF - Communications in Mathematical Physics

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Conformally Covariant Bi-differential Operators for Differential Forms

Abstract

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