Covariant bi-differential operators on matrix space  [ Opérateurs bi-différentiels sur l’espace des matrices ]
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,)×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.

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).

Reçu le : 2016-01-26
Révisé le : 2016-08-28
Accepté le : 2016-10-26
Publié le : 2017-09-25
DOI : https://doi.org/10.5802/aif.3114
Classification : 22E45,  58J70
Mots clés : Opérateurs différentiels covariants, opérateurs d’entrelacement de Knapp–Stein, équation fonctionnelle de Zeta, transvectants, crochets de Rankin–Cohen
@article{AIF_2017__67_4_1427_0,
     author = {Clerc, Jean-Louis},
     title = {Covariant bi-differential operators on matrix space},
     journal = {Annales de l'Institut Fourier},
     pages = {1427--1455},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {4},
     year = {2017},
     doi = {10.5802/aif.3114},
     language = {en},
     url = {www.numdam.org/item/AIF_2017__67_4_1427_0/}
}
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. http://www.numdam.org/item/AIF_2017__67_4_1427_0/

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