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The U(1)-Kepler Problems

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.3527268· OSTI ID:21501211
 [1]
  1. Department of Mathematics, Hong Kong Univ. of Sci. and Tech., Clear Water Bay, Kowloon (Hong Kong)
Let n{>=} 2 be a positive integer. To each irreducible representation {sigma} of U(1), a U(1)-Kepler problem in dimension (2n-1) is constructed and analyzed. This system is superintegrable and when n= 2 it is equivalent to a MICZ-Kepler problem. The dynamical symmetry group of this system is U-tilde(n,n), and the Hilbert space of bound states H({sigma}) is the unitary highest weight representation of U-tilde(n,n) with the minimal positive Gelfand-Kirillov dimension. Furthermore, it is shown that the correspondence between {sigma}* (the dual of {sigma}) and H({sigma}) is the theta-correspondence for dual pair (U(1),U(n,n))sub set of p{sub 4n}(R).
OSTI ID:
21501211
Journal Information:
Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
Country of Publication:
United States
Language:
English

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