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Rankin–Cohen brackets
on tube-type domains
Jean-Louis Clerc |
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Vol. 3 (2021), No. 3, 551–569
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Abstract |
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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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Keywords
tube-type domain, Euclidean Jordan algebra, holomorphic
discrete series, tensor product, weighted Bergman space,
Rankin–Cohen brackets, Jacobi polynomials
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Mathematical Subject Classification 2010
Primary: 22E46
Secondary: 32M15, 33C45
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Milestones
Received: 12 March 2020
Revised: 26 March 2020
Accepted: 23 July 2020
Published: 13 May 2021
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Authors |
| Jean-Louis Clerc | |
| Institut Elie Cartan, CNRS Université de Lorraine Campus V. Grignard Nancy France |
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