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Recently Pluhar and Weidenmueller [Ann. Phys. (N.Y.) Vol 297, 344 (2002)]showed that the eigenvectors of the matrix of second moments of embeddedGaussian unitary ensemble of random matrices generated by k-body interactions(EGUE(k)) for m fermions in N single particle states are SU(N) Wignercoefficients and derived also an expression for the eigenvalues. Going beyondthis work, we will show that the eigenvalues of this matrix are square of aSU(N) Racah coefficient and thus the matrix of second moments of EGUE(k) issolved completely by SU(N) Wigner-Racah algebra.Comment: 16 page

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