Superconducting pairing in non-pseudospin electron bands

We develop the symmetry classification of superconducting gap functions in electron bands that do not transform like the pure spin-1/2 states under the crystal point group operations. Generalizing the commony used Ueda-Rice prescription, we define the Bloch bases in twofold degenerate bands with spin-orbit coupling in a way which satisfies all symmetry and continuity requirements. These bases are used to construct general multiband pairing Hamiltonians in centrosymmetric crystals. Focusing on single band pairing, several exceptional cases are identified in which the triplet superconducting gap function does not transform under the point-group operations as a pseudovector, with a significant impact on the nodal structure.