Algebraization of difference eigenvalue equations related to Uq(sl2)

P. B. Wiegmann, A. X. Zabrodin

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


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 polynoms (discrete polynoms). Such difference operators can be constructed by means of Uq(sl2) the quantum deformation of the sl2 algebra. The roots of the polynoms determine the spectrum and obey the Bethe ansatz equations. A particular case of difference equations for q-hypergeometric and Askey-Wilson polynoms is discussed. Applications to the problem of Bloch electrons in a magnetic field are outlined.

Original languageEnglish
Pages (from-to)699-724
Number of pages26
JournalNuclear Physics B
Issue number3
Publication statusPublished - 2 Oct 1995
Externally publishedYes


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