30 citations · 53 across the 7 of their papers we have counts for
7 papers
Krall-type orthogonal polynomials and integrable isomonodromic deformations
Luc Haine
Krall-type polynomials are orthogonal polynomials for a Stieltjes' measure obtained by adding jumps at the boundary of the orthogonality interval of either the generalized Laguerre…
On a generalization of Jacobi's elegantissima
Luc Haine
We establish a generalization of Jacobi's elegantissima, which solves the pendulum equation. This amazing formula appears in lectures by the famous cosmologist Georges Lemaître, du…
A Centerless Virasoro Algebra of Master Symmetries for the Ablowitz-Ladik Hierarchy
Luc Haine, Didier Vanderstichelen
We show that the (semi-infinite) Ablowitz-Ladik (AL) hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner [Progr. Theoret. Phys. 70 (198…
A centerless representation of the Virasoro algebra associated with the unitary circular ensemble
Luc Haine, Didier Vanderstichelen
We consider the 2-dimensional Toda lattice tau functions deforming the probabilities that a randomly chosen matrix from the unitary group U(n), for the Ha…
Trigonometric Darboux transformations and Calogero-Moser matrices
Luc Haine, Emil Horozov, Plamen Iliev
We characterize in terms of Darboux transformations the spaces in the Segal-Wilson rational Grassmannian, which lead to commutative rings of differential operators having coefficie…
KP Trigonometric Solitons and an Adelic Flag Manifold
Luc Haine
We show that the trigonometric solitons of the KP hierarchy enjoy a differential-difference bispectral property, which becomes transparent when translated on two suitable spaces of…
Askey-Wilson Type Functions, With Bound States
Luc Haine, Plamen Iliev
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified s…