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q-Ultraspherical polynomials for q a root of unity

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arxiv q-alg/9605033 v1 pith:Q2ELWUKX submitted 1996-05-21 q-alg math.QA

V.Spiridonov (Univ. de Montreal) , A.Zhedanov (Donetsk Univ) This is my paper · ORCID
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keywords polynomialsrootunityalgebraanalogsbetaclasscondition
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abstract

Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of $q$-beta integrals of Ramanujan.

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    Spectral surgery on a uniform XX chain yields analytic spin chains that interpolate between uniform and Krawtchouk chains and achieve good-fidelity state transfer with bounded couplings.

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