Asao Arai
 Representations of the Quantum Plane and the Quantum Algebra 
$U_{q}({\rm sl}_2)$ on $L^2(\R^d)$
(32K, Latex2e)

ABSTRACT.  A 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 two-dimensional quantum system with a 
magnetic field concentrated on an infinite lattice.