fluids: the EPDiff dual pair due to Holm and Marsden, and the ideal fluid dual pair due to Marsden and Weinstein.
under a O(2n)-symmetry and has used this quotient to describe the relationship between two different parametrisations of Gaussian wave packet dynamics commonly used in semiclassical mechanics. In this paper, we suggest a new interpretation of (a subset of) the unreduced space as
being the frame bundle F(T ?Rn) of T ?Rn. We outline some advantages of this interpretation and explain how it can be extended to more general symplectic manifolds using the notion of the diagonal lift of a symplectic form due to Cordero and de León (Rend Circ Mat Palermo 32:236?271, 1983).