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

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 Title: Representations of the Quantum Plane and the Quantum Algebra $U_{q}({\rm sl}_2)$ on $L^2(\R^d)$ Authors: Arai, Asao Browse this author Keywords: quantum plane quantum algebra singular magnetic field Issue Date: 17-Aug-2007 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 868 Start Page: 1 End Page: 13 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69677 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics