THE Sp(1)-KEPLER PROBLEMS

Let n ≥ 2 be a positive integer. To each irreducible representation σ of Sp(1), an Sp(1)-Kepler problem in dimension (4n− 3) is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a generalized MICZ-Kepler problem in dimension five. The dynamical symmetry group of this system is e O∗(4n) with the Hilbert space of bound states H (σ) being the unitary highest weight representation of f O(4n) with highest weight (−1, · · · ,−1 | {z }