Vol. 3, No. 3, 2021
Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2576-7666 (online)
ISSN 2576-7658 (print)
Author index
To appear
 
Other MSP Journals
Rankin–Cohen brackets on tube-type domains

Jean-Louis Clerc
Vol. 3 (2021), No. 3, 551–569
DOI: 10.2140/tunis.2021.3.551
Abstract

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.

Keywords
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
Milestones
Received: 12 March 2020
Revised: 26 March 2020
Accepted: 23 July 2020
Published: 13 May 2021
Authors
Jean-Louis Clerc
Institut Elie Cartan, CNRS
Université de Lorraine
Campus V. Grignard
Nancy
France