  A theory for the transitive action of a group on the configuration space of a
system of particles is shown to lead to the conclusion that interactions can be
represented by the action of cosets of the group. By application of this
principle to Pauli spinors, the symplectic group Sp(n) is shown to be the
largest group of isometries of the space. Interactions between particles are
represented by the complete quaternionic flag variety Sp(n)/Sp(1)^n.
