Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773289 | Linear Algebra and its Applications | 2017 | 33 Pages |
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 N=2 or q=i.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
P. Baseilhac, A.M. Gainutdinov, T.T. Vu,