U(2Ω)⊃U(Ω)⊗SU(2) Wigner-Racah algebra for embedded Gaussian unitary ensemble of random matrices with spin

Exact results for embedded Gaussian unitary ensemble of two-body interactions for fermions with spin [EGUE(2)-s] are derived using the Wigner-Racah algebra of the embedding U(2 Omega)superset of U(Omega)circle times SU(2) algebra. Explicit formulas, for systems with m fermions and spin S, are given for the lower order cross correlations, between states with (m,S) and (m',S'), generated by this ensemble and also, in terms of a SU(Omega) Racah coefficient, for the fourth order shape parameter for the fixed-(m,S) density of states. (c) 2007 American Institute of Physics.