Abstract
In this paper we study the triple reduced product of three coadjoint orbits of SU(3) and show that, under suitable hypotheses on the parameters, it is homeomorphic to S2. Hence by Moser’s method it is symplectomorphic to a copy of S2 whose symplectic volume equals that of the triple reduced product.
We outline a method to find a Hamiltonian function on this S2 (with its non-standard symplectic form) which is the moment map for a circle action. In other words the period of the Hamiltonian flow is constant except at fixed points.
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Jeffrey, L., Rayan, S., Seal, G., Selick, P., Weitsman, J. (2018). The Triple Reduced Product and Hamiltonian Flows. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXV . Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-63594-1_6
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DOI: https://doi.org/10.1007/978-3-319-63594-1_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-63593-4
Online ISBN: 978-3-319-63594-1
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