2 citations · 3 across the 17 of their papers we have counts for
22 papers
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…
Para families of orthogonal polynomials
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, -para-Racah and para-Bannai--Ito polynomials followed, obtained…
The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Bannai--Ito polynomials are orthogonal on a Bannai--Ito bi-lattice that is \emph{two-sided} --- it extends on both sides of a central value --- and depend, besides t…
The para--Racah Hamiltonian as an exactly solvable discretization of the Pöschl--Teller box
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter, define through their recurrence relation a mirror-symmetric tridiagonal Hami…
The para--Krawtchouk oscillator and its continuum limit
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that exhibits fractional revival. We determine the continuum limit of this Hami…
Universal scaling of spatially extended zero modes in inhomogeneous SSH chains
Gilles Parez, Nicolas Crampé, Quentin Labriet +2
Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this pict…
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…
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…
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…
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…
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…
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 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 …
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…
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…
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…
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…