Gg. Athanasiu et Eg. Floratos, THE LIGHTCONE SUQ(2) QUANTUM ALGEBRA AS DYNAMICAL SYMMETRY OF THE AZBEL-HOFSTADTER PROBLEM, Physics letters. Section B, 352(1-2), 1995, pp. 105-110
Resent investigations on the quantum group symmetry of the Bloch elect
ron in a magnetic field of rational flux by Wiegmann and Zabrodin and
Faddeev and Kashaev lead to generalised Bethe-ansatz like equations on
high genus algebraic curves. We investigate another manifestation of
this symmetry directly at the quantum algebra level, where the Cartesi
an SUq(2) algebra for values of q, roots of unity, appears on the ligh
t cone frame of the lattice. The Askey-Wilson polynomials and the fini
te quantum mechanics formalism are shown to be important elements of t
he problem.