Publications (15)
Algebraic interpretation of discrete families of matrix valued orthogonal polynomials
Quentin Labriet, Lucia Morey, Luc Vinet
An algebraic interpretation of matrix-valued orthogonal polynomials (MVOPs) is provided. The construction is based on representations of a (-deformed) Lie algebra …
Bispectral rational functions and Leonard trios
Nicolas Crampé, Wolter Groenevelt, Quentin Labriet +3
It is well-known that Leonard pairs have a close connection with bispectral orthogonal polynomials of the Askey scheme. In this paper, we introduce the notion of a Leonard trio $(V…
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…
The dynamical algebra of the generic superintegrable model on the two-sphere
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of…
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 p…
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…
Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet +2
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jorda…
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…
Inhomogeneous SSH models and the doubling of orthogonal polynomials
Nicolas Crampé, Quentin Labriet, Lucia Morey +2
We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of th…
Algebraic Leonard trio approach to rational functions: the Hahn case
Nicolas Crampé, Quentin Labriet, Lucia Morey +1
The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn a…
Holographic transform for tensor product of holomorphic discrete series
Quentin Labriet
We study holographic operators associated with Rankin-Cohen brackets which are symmetry breaking operators for the restriction of tensor products of holomorphic discrete series of…
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}…
Meta Algebras and Special Functions: the Racah Case
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its…
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…