Complete ladder sets for $U(6, 6)$

Complete sets of commuting (symmetric) operators which, belong to the enveloping algebra of an arbitrary ladder representation of the group $U(6, 6)$ are considered. These sets are independent and each of them includes the operators $B, n, Y, Z, I^2, I_3, J^2, J_3$ which possess a definite physical interpretation [3]. The proof of the completeness of the considered sets is the main result of the work. Besides this, a method is given for the construction of all common eigenvectors of each complete set.