# Representations of the Quantum Plane and the Quantum Algebra $U_{q}({\rm sl}_2)$ on $L^2(\R^d)$

Preprint Series # 868
Arai, Asao Representations of the Quantum Plane and the Quantum Algebra $U_{q}({\rm sl}_2)$ on $L^2(\R^d)$. (2007);

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

Item Type: Preprint 20 quantum plane, quantum algebra, singular magnetic field 81-xx QUANTUM THEORY 1762