Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

Autor:	Baseilhac, P., Gainutdinov, A. M., Vu, T. T.
Rok vydání:	2016
Předmět:	Mathematics - Quantum Algebra Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Representation Theory
Zdroj:	Linear Algebra and its Applications 522 (2017) 71-110
Druh dokumentu:	Working Paper
Popis:	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 are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at N=2 or q=i. Comment: 32 pages; v2: Appendices improved and extended, e.g. a proof of irreducibility is added; v3: version for Linear Algebra and its Applications, one assumption added in Appendix about eq. (A.2)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1607.00606 Zobrazit plný text záznamu View this record from Arxiv