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The O(1)-Kepler problems

Authors Meng, Guowu View this author's profile
Issue Date 2008
Source Journal of Mathematical Physics , v. 49, (10), Oct 2008, article number 102111
Summary Let n >= 2 be an integer. To each irreducible representation sigma of O(1), an O(1)-Kepler problem in dimension n is constructed and analyzed. This system is super integrable and when n=2 it is equivalent to a generalized MICZ (McIntosh-Cisneros-Zwanziger)-Kepler problem in dimension 2. The dynamical symmetry group of this system is (Sp) over tilde (2n,R) with the Hilbert space of bound states H(sigma) being the unitary highest weight representation of (Sp) over tilde (2n,R) with highest weight [GRAPHICHS] which occurs at the rightmost nontrivial reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. (Here vertical bar sigma vertical bar=0 or 1 depending on whether sigma is trivial or not.) Furthermore, it is shown that the correspondence sigma <-> H(sigma) is the theta correspondence for dual pair (O(1), Sp(2n,R)) subset of Sp(2n,R). (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3000062]
ISSN 0022-2488
Rights Journal of Mathematical Physics © copyright 2008 American Institutes of Physics. The journal's web site is located at
Language English
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