Space group approach to the wavefunction of a Cooper pair

The method of construction of the wavefunction of a Cooper pair based on the Pauli exclusion principle and the Mackey-Bradley theorem is developed. Tables of symmetrized and antisymmetrized Kronecker squares of single- and double-valued irreducible representations of the groups O h 6 and D 6h 4 are obtained. The tables are used to search for points in the Brillouin zone where totally symmetric Cooper pairs can exist. It is shown that, in the symmetrical points and directions in a Brillouin zone, a direct connection between the multiplicity and parity of the Cooper pair wavefunction does not exist.