Event
Pascal Baseilhac, Universit茅 de Tours
Tuesday, November 15, 2016 15:30to16:30
Room 4336, Pavillon Andr茅-Aisenstadt, 2920, Chemin de la tour, 5th floor, Montreal, QC, H3T 1J4, CA
Title: Cyclic tridiagonal pairs, higher order Onsager algebras and othogonal polynomials.
Abstract: The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is identified as a higher-order generalization of the Onsager algebra. It can be viewed as a subalgebra of the q-Onsager algebra for a proper specialization at q the primitive 2Nth root of unity. Orthogonal polynomials beyond the Leonard duality introduced by Tsujimoto, Vinet and Zhedanov are revisited in light of this framework. Joint work with A.M Gainutdinov and T.T. Vu. arXiv:1607.00606 [math.QA]