U(N) coherent states for loop quantum gravity

We investigate the geometry of the space of N-valent SU(2) intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners. (C) 2011 American Institute of Physics. [doi:10.1063/1.3587121]