Vol. 3, No. 3, 2021

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Rankin–Cohen brackets on tube-type domains

Jean-Louis Clerc

Vol. 3 (2021), No. 3, 551–569

A new formula is obtained for the holomorphic bidifferential operators on tube-type domains which are associated to the decomposition of the tensor product of two scalar holomorphic representations, thus generalizing the classical Rankin–Cohen brackets. The formula involves a family of polynomials of several variables which may be considered as a (weak) generalization of the classical Jacobi polynomials.

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tube-type domain, Euclidean Jordan algebra, holomorphic discrete series, tensor product, weighted Bergman space, Rankin–Cohen brackets, Jacobi polynomials
Mathematical Subject Classification 2010
Primary: 22E46
Secondary: 32M15, 33C45
Received: 12 March 2020
Revised: 26 March 2020
Accepted: 23 July 2020
Published: 13 May 2021
Jean-Louis Clerc
Institut Elie Cartan, CNRS
Université de Lorraine
Campus V. Grignard