Abstract
Unit adjoint tensor operators in SO(n) have been obtained, and the eigenvalues of the invariants connected with them evaluated. These adjoint tensor operators are keys to the solution of the multiplicity problem of the Wigner coefficients of SO(n). These adjoint tensor operators are used in the calculation of the Wigner coefficients of SO(5) in the direct product of the 10-dimensional representation with an arbitrary representation. The results agree with Hecht [K. T. Hecht, Nucl. Phys. 63, 177 (1965)].