no. 4
Covariant bi-differential operators on matrix space
[Opérateurs bi-différentiels sur l’espace des matrices]
Clerc, Jean-Louis1
1 Institut Élie Cartan, Université de Lorraine 54506 Vandœuvre-lès Nancy (France)
Annales de l'Institut Fourier, Tome 67 (2017) no. 4, pp. 1427-1455.

On construit une famille d’opérateurs bi-différentiels de C ∞ (Mat(m,ℝ)×Mat(m,ℝ)) dans C ∞ (Mat(m,ℝ)) qui sont covariants pour l’action projective du groupe SL(2m,ℝ) sur Mat(m,ℝ). Dans le cas m=1, cette construction fournit une nouvelle approche des transvectants et des crochets de Rankin–Cohen.

A family of bi-differential operators from C ∞ (Mat(m,ℝ)×Mat(m,ℝ)) into C ∞ (Mat(m,ℝ)) which are covariant for the projective action of the group SL(2m,ℝ) on Mat(m,ℝ) is constructed, generalizing both the transvectants and the Rankin–Cohen brackets (case m=1).

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DOI : 10.5802/aif.3114
Classification : 22E45, 58J70
Keywords: Covariant differential operators, Knapp–Stein intertwining operators, Zeta functional equation, transvectants, Rankin–Cohen brackets
Mot clés : Opérateurs différentiels covariants, opérateurs d’entrelacement de Knapp–Stein, équation fonctionnelle de Zeta, transvectants, crochets de Rankin–Cohen
Clerc, Jean-Louis 1

1 Institut Élie Cartan, Université de Lorraine 54506 Vandœuvre-lès Nancy (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Clerc, Jean-Louis. Covariant bi-differential operators on matrix space. Annales de l'Institut Fourier, Tome 67 (2017) no. 4, pp. 1427-1455. doi : 10.5802/aif.3114. https://aif.centre-mersenne.org/articles/10.5802/aif.3114/

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