Representations of the Quantum Plane and the Quantum Algebra $U_{q}({\rm sl}_2)$ on $L^2(\R^d)$Preprint Series # 868
AbstractA class of representations on the Hilbert space $L^2(\R^d)$ ($d\geq 2$) of the quantum plane $\C_q^2$ and the quantum algebra $U_q({\rm sl}_2)$ 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 twodimensional quantum system with a magnetic field concentrated on an infinite lattice.
