MODERN PHYSICS LETTERS A, vol.11, no.14, pp.1139-1149, 1996 (SCI-Expanded)
Casimir W-algebras are shown to exist in such a way that the conformal spins of primary (generating) fields coincide with the orders of independent Casimir operators. We show here that this coincidence can be extended further to the case that these generating fields have the same eigenvalues with the Casimir operators.