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arXiv · 2304.10803

Identities for Rankin-Cohen brackets, Racah coefficients and associativity

Quentin Labriet·Loic Poulain d'Andecy
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Abstract

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 D.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.

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Quentin Labriet, Loic Poulain d'Andecy. 2023-04-21. Identities for Rankin-Cohen brackets, Racah coefficients and associativity. https://arxiv.org/abs/2304.10803

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