Covariant bi-differential operators on matrix space
Annales de l'Institut Fourier, Volume 67 (2017) no. 4, pp. 1427-1455.

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

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

Published online:
DOI: 10.5802/aif.3114
Classification: 22E45, 58J70
Keywords: Covariant differential operators, Knapp–Stein intertwining operators, Zeta functional equation, transvectants, Rankin–Cohen brackets
Clerc, Jean-Louis 1

1 Institut Élie Cartan, Université de Lorraine 54506 Vandœuvre-lès Nancy (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Clerc, Jean-Louis. Covariant bi-differential operators on matrix space. Annales de l'Institut Fourier, Volume 67 (2017) no. 4, pp. 1427-1455. doi : 10.5802/aif.3114.

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