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Title: The O(1)-Kepler problems
Authors: Meng, Guo-Wu
Keywords: Bound states
Celestial mechanics
Dynamical symmetry
Hilbert spaces
Kepler problem
Issue Date: 21-Oct-2008
Citation: Journal of mathematical physics, v. 49, iss. 10, p. 102111, 2008
Abstract: Let n≥2 be an integer. To each irreducible representation σ 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 Sp͠(2n,R) with the Hilbert space of bound states H(σ) being the unitary highest weight representation of Sp͠(2n,R) with highest weight which occurs at the rightmost nontrivial reduction point in the Enright–Howe–Wallach classification diagram for the unitary highest weight modules. (Here lσl=0 or 1 depending on whether σ is trivial or not.) Furthermore, it is shown that the correspondence σ↔H(σ) is the theta correspondence for dual pair (0(1) ,Sp(2n,R))⊆Sp(2n,R).
Rights: Journal of Mathematical Physics © copyright 2008 American Institutes of Physics. The journal's web site is located at
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