The quantum numbers are generally associated with discrete energy states for  electrons in an atomic structure.  Brillouin zone, however, is associated with a system of atom forming for  example a specific crystal structure with a particular symmetry.  This leads to the formation of the energy band diagram associated the collective behavior of similar electron in the crystalline structure.  Under such conditions perhaps the quantum numbers of electrons participating in forming energy band diagrams that energy wise fall within Brillouin zone for a particular crystalline structure might be consider in your analysis.

thank you Bahram Roughani for your response ..

Block wave function that is characterized by k  wave vector  has energy eigenvalues  for the periodic potential problem are periodic in the reciprocal lattice :  E k+G  = E k  thus to label the eigenvalues uniquely it is necessary to restrict  k  to a primitive cell of the reciprocal lattice. Even though we might select the primitive unit cell in many ways but the one used in practice is called the Brillouin zone or the first Brillouin Zone. There are certain useful symmetry properties of the Hamiltonian for the periodic lattice depending upon  what the space group of the crystal structure (Bravais Lattice) belongs plus the operation of the time reversal. Also we recall that the lattice as well as the Hamiltonian is invariant under the translations, T.    Namely:

 T   Phik  = Exp (i k t) Phik . 

The point group symmetry of the lattice  is characterized in the Brillouin zone by the existence of the  certain special points and lines , which are labelled with Latin  and Greek capital letters. These letters are used in the reduced zone scheme for free electrons to designate the various energy levels associate for given k  vector in certain crystallographic directions as well their degeneracy.

For full  cubic  point group is denoted by   4 / m 3^  2/m. In simple cubic lattice there are four special points R, M, X , L and five special lines  Del, S , T , Sıgma ;Z .

Thanks a lot Tarik Ömer Oğurtani  for your answer.