SU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices

Recently Pluhar and Weidenmueller [Ann. Phys. (N.Y.) Vol 297, 344 (2002)] showed that the eigenvectors of the matrix of second moments of embedded Gaussian unitary ensemble of random matrices generated by k-body interactions (EGUE(k)) for m fermions in N single particle states are SU(N) Wigner coefficients and derived also an expression for the eigenvalues. Going beyond this work, we will show that the eigenvalues of this matrix are square of a SU(N) Racah coefficient and thus the matrix of second moments of EGUE(k) is solved completely by SU(N) Wigner-Racah algebra.