SO*(2N) coherent states for loop quantum gravity

Understand

A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d).

• We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N).
• This group can be viewed as the subgroup of the symplectic group Sp(4N,R) which preserves the SU(2) invariance.
• We construct the associated Perelomov coherent states and discuss the notion of semi-classical limit, which is more subtle that we could expect.