Identities for Rankin–Cohen brackets, Racah coefficients and associativity

We prove an infinite family of identities satisfied by the Rankin–Cohen brackets involving the Racah polynomials. A natural interpretation in the representation theory of sl (2) is provided. From these identities and known properties of the Racah polynomials follows a short new proof of the associat...

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Bibliographic Details
Published in:Letters in mathematical physics 2024-01, Vol.114 (1), Article 20
Main Authors: Labriet, Q., Poulain d’Andecy, L.
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We prove an infinite family of identities satisfied by the Rankin–Cohen brackets involving the Racah polynomials. A natural interpretation in the representation theory of sl (2) is provided. From these identities and known properties of the Racah polynomials follows a short new proof of the associativity of the Eholzer product. Finally, we discuss, in the context of Rankin–Cohen algebras introduced by Zagier, how any algebraic identity satisfied by the Rankin–Cohen brackets can be seen as a consequence of the set of identities presented in this paper.
ISSN:1573-0530
1573-0530
DOI:10.1007/s11005-023-01763-y