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math.RT2023
Identities for Rankin-Cohen brackets, Racah coefficients and associativity
Quentin Labriet, Loic Poulain d'Andecy
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…
math.RT2023
Realisations of Racah algebras using Jacobi operators and convolution identities
Q. Labriet, L. Poulain d'Andecy
Using the representation theory of sl(2) and an appropriate model for tensor product of lowest weight Verma modules, we give a realisation first of the Hahn algebra, and then of th…
math.RT2023
Restricting holomorphic discrete series representations to a compact dual pair
Jan Frahm, Quentin Labriet
The goal of this article is to study the branching problem for a holomorphic discrete series representation of the conformal group of a simple Euclidean Jordan algebra restrict…