Abstract
A finite projective geometry T = PG (n ,2) is associated with any coupling-recoupling (N -jm ) coefficient of SU (2). This geometry is based on a duality of projective spaces and a discrete Fourier transform. An angular momentum jk with projection Mk is attached at each point k T . Some of these momenta and projections are specified by the arguments of the N -jm coefficient. The others are qualified as hidden. The value of the N -jm coefficient is given in terms of a summation over the hidden angular momenta and hidden projections of a `full pn -JM symbol' with a high degree of symmetry. For the 3-j coefficient (Clebsch-Gordan or Wigner coefficient), the finite projective geometry is a line of three points with one hidden projection and the formula of hidden momenta gives an interpretation of the combinatorial formula of Racah for the 3-j coefficient.
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