Algebraization of difference eigenvalue equations related to $U_q(s{l}_2)$

Abstract

A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polinomials (discrete polinomials). Such difference operators can be constructed by means of $U_q(s{l}_2)$, the quantum deformation of the $s{l}_2$ algebra. The roots of polinomials determine the spectrum and obey the Bethe Ansatz equations. A particular case of difference equations for $q$-hypergeometric and Askey-Wilson polinomials is discussed. Applications to the problem of Bloch electrons in magnetic field are outlined. {abstract}

34 pages, LATEX

References in corpus (3)

• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
• Degenerations of Sklyanin algebra and Askey-Wilson polynomials
• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Bloch Electrons in a Magnetic Field

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