Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal
  polynomials   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.

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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex