 07198 Asao Arai
 Representations of the Quantum Plane and the Quantum Algebra
$U_{q}({\rm sl}_2)$ on $L^2(\R^d)$
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Aug 17, 07

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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 twodimensional quantum system with a
magnetic field concentrated on an infinite lattice.
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