Identities for Rankin-Cohen brackets, Racah coefficients and associativity
Representation Theory
2023-04-24 v1 Classical Analysis and ODEs
Number Theory
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.
Keywords
Cite
@article{arxiv.2304.10803,
title = {Identities for Rankin-Cohen brackets, Racah coefficients and associativity},
author = {Quentin Labriet and Loic Poulain d'Andecy},
journal= {arXiv preprint arXiv:2304.10803},
year = {2023}
}
Comments
14 pages