Séminaire de Physique Théorique
Bispectral q-hypergeometric basis, q-Onsager algebra and integrable systemsPascal Baseilhac (LMPT)
Thursday 19 November 2015 14:00 - Tours - Salle 1180 (Bât E2)
Résumé :
By analogy with the elementary example of the harmonic oscillator, of Calogero-Sutherland-Moser integrable models or the open Toda chain for which a (q-)hypergeometric formulation of the Hamiltonian’s eigenfunctions is known (in terms of one-variable Hermite polynomials, multi-variable Macdonald-Koornwinder or limiting cases (q-)Wittaker or Hall-Littlewood), I will show that the bispectral family of multivariable Gasper-Rahman polynomials (generalizing those of Askey-Wilson) provide a q-hypergeometric basis for the Hamiltonian’s eigenfunctions of the class of quantum integrable models generated from the q-Onsager algebra (ex: Ising, superintegrable chiral Potts, XY, open XXZ,...). In this talk, I will present an overview on the subject and the main results. Work done in collaboration with Xavier Martin. See: arXiv:1506.06902.
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