Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

Baseilhac, P.; Vu, T. T.; Gainutdinov, Azat

doi:10.1016/j.laa.2017.02.009

Journal Article

PUBDB-2018-00632

Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

Baseilhac, P. (Corresponding author) ; Gainutdinov, A.DESY* ; Vu, T. T.

2017
Elsevier New York, NY

Linear algebra and its applications 522, 71 - 110 (2017) [10.1016/j.laa.2017.02.009]

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Please use a persistent id in citations: doi:10.1016/j.laa.2017.02.009 doi:10.3204/PUBDB-2018-00632

Report No.: Hamburger Beitr ̈age zur Mathematik 595; ZMP-HH-16-10; arXiv:1607.00606

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 are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at or $N = 2$ $or$ $q = i$.

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