The Sp(1)-Kepler problems
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong)
Let n{>=}2 be a positive integer. To each irreducible representation {sigma} of Sp(1), an Sp(1)-Kepler problem in dimension (4n-3) is constructed and analyzed. This system is superintegrable, and when n=2 it is equivalent to a generalized MICZ-Kepler problem in dimension of 5. The dynamical symmetry group of this system is O-tilde*(4n) with the Hilbert space of bound states H({sigma}) being the unitary highest weight representation of O*-tilde(4n) with highest weight, (-1,{center_dot}{center_dot}{center_dot},-1,-(1+{sigma})), which occurs at the rightmost nontrivial reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. Here {sigma} is the highest weight of {sigma}. Furthermore, it is shown that the correspondence {sigma}{r_reversible}H({sigma}) is the theta-correspondence for dual pair (Sp(1),O*(4n))subset Sp(8n,R)
- OSTI ID:
- 21294209
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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