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Representations of the Quantum Plane and the Quantum Algebra $U_{q}({\rm sl}_2)$ on $L^2(\R^d)$
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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