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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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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84018

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

Submitter: 数学紀要登録作業用

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