On The Construction of W(N)-Algebras In The Form Of A(N-1)-Casimir   Algebras
  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 eiginvalues with the Casimir operators. 
H.T. Ozer