Algebraization of difference eigenvalue equations related to $U_q(sl_2)$

Details Algebraization of difference eigenvalue equations related to $U_q(sl_2)$ Algebraization of difference eigenvalue equations related to $U_q(sl_2)$

1995-01-27

arxiv.org/abs/cond-mat/9501129v1

Nucl.Phys. B451 (1995) 699

Physics

Condensed Matter

34 pages, LATEX

Scientific paper

10.1016/0550-3213(95)00361-U

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 $U_q(sl_2)$, the quantum deformation of the $sl_2$ 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}

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