Covariant bi-differential operators on matrix space
Annales de l'Institut Fourier, Volume 67 (2017) no. 4, p. 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.
Received : 2016-01-27
Revised : 2016-08-29
Accepted : 2016-10-27
Published online : 2017-09-26
Classification:  22E45,  58J70
Keywords: Covariant differential operators, Knapp–Stein intertwining operators, Zeta functional equation, transvectants, Rankin–Cohen brackets
     author = {Clerc, Jean-Louis},
     title = {Covariant bi-differential operators on matrix space},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {4},
     year = {2017},
     pages = {1427-1455},
     doi = {10.5802/aif.3114},
     language = {en},
     url = {}
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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