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Continuous representations of the meta Hahn algebra and special functions
Quentin Labriet, Luc Vinet
Infinite families of biorthogonal rational functions are constructed using infinite dimensional representations of the three-generated meta Hahn algebra. Continuous Hahn and contin…
Exceptional theta correspondences via Plancherel formulas for rank one symmetric spaces
Jan Frahm, Quentin Labriet
We consider the minimal representation of (a finite cover of) the conformal group of a simple split Jordan algebra over or , whenever it exists. The confor…
Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is used to provide an interpretation of the two-variable Jacobi polynomials on the triangle, as overlaps betwee…
Little -Jacobi polynomials and symmetry breaking operators for
Quentin Labriet, Loïc Poulain d'Andecy
This paper presents explicit formulas for intertwining operators of the quantum group acting on tensor products of Verma modules. We express a first set of intertwining…
Differential symmetry breaking operators for the pair
Jonathan Ditlevsen, Quentin Labriet
In this article we study differential symmetry breaking operators between principal series representations induced from minimal parabolic subgroups for the pair $(\operatorname{GL}…
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…
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…
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…
A geometrical point of view for branching problems for holomorphic discrete series of conformal Lie groups
Quentin Labriet
This article is devoted to branching problems for holomorphic discrete series representations of a conformal group of a tube domain over a symmetric cone . More pr…