Admissible complete sets in ladder $U(6,6)$-symmetry

The notion of an admissible set is introduced in a natural manner. Each such set is complete and contains the observables $B,n,Y,Z,\mathbf I^2,I_3,\mathbf J^2,J_3$ (where $B$ is the baryon number, $Y$ is the hypercharge, $n$ and $Z$ are quark numbers$\footnote{More precisely, $n$ defines the number of quarks and $Z$ the number of normal quarks. However, it is not necessary to use quark language. The~important thing is [1,2] that $n$ gives the rungs of the ladders and $Z$ the physical ladders, $n$ being associated with the ordinary parity and $Z$ with some additional parity~[4].}$, and $J$ and $I$ are, respectively, the spin and isospin). One main class of admissible sets is distinguished and studied. It is infinite, and its sets can be “enumerated” by means of continuous parameters. Particular attention is devoted to the proof that these sets are complete.