Symmetry properties of the k-body embedded unitary Gaussian ensemble of random matrices

We extend the recent study of the k-body embedded Gaussian ensembles by L. Benet, T. Rupp. and H. A. Weidenmuller (2001. Benet. Phys. Rev. Lett. 87, 101601-1 and 2001, Aim. Phys. (N.Y.) 292. 67) and by T Asaga. L. Benet. T. Rupp. and H. A. Weidenmuller (cond-mat/0107363 and condmat/0107364). We show that central results of these papers can be derived directly from the symmetry properties of both the many-particle states and the random k-body interaction. We offer new insight into the structure of the matrix of second moments of the embedded ensemble and of the supersymmetry approach. We extend the concept of the embedded ensemble and define it purely group- theoretically. (C) 2002 Elsevier Science (USA)