A class of Hilbert space representations of the quantum plane and the quantum algebra Uq(sl2)

A class of representations on the Hilbert space L2(ℝd) (d ≥ 2) of the quantum plane ℂ q 2 and the quantum algebra Uq (sl2) is presented. The boundedness and the unboundedness of the representations are discussed. A physically interesting example of the representations is shown to appear in a two-dimensional quantum system with a magnetic field concentrated on an infinite lattice.