Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/6042
The O(1)Kepler problems
Authors  Meng, Guowu  

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 (McIntoshCisnerosZwanziger)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 EnrightHoweWallach 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]  
Subjects  
ISSN  00222488  
Rights  Journal of Mathematical Physics © copyright 2008 American Institutes of Physics. The journal's web site is located at http://jmp.aip.org  
Language  English 

Format  Article  
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