The classification and dynamics of the momentum polytopes of the SU(3) action on points in the complex projective plane with an application to point vortices
Amna Shaddad · MIMS EPrints (University of Southampton) · 2018
We have fully classified the momentum polytopes of the SU(3) action on CP2 x CP2 and CP2 x CP2 x CP2, both actions with weighted symplectic forms, and their corresponding transition momentum polytopes. For CP2 x CP2 the momentum polytopes are distinct line segments. The action on CP2 x CP2 x CP2 has 8 different momentum polytopes. The vertices of the momentum polytopes of the SU(3) action on CP2 x CP2 x CP2 fall into two categories: definite and indefinite vertices. The reduced space corresponding to momentum map image values at definite vertices is isomorphic to the 2-sphere. We show that these results can be applied to assess the dynamics by introducing and computing the space of allowed velocity vectors for the different configurations of two-vortex systems.