  Recent development in exact classification of a superconducting gap has
elucidated various unconventional gap structures, which have not been predicted
by the classification of order parameter based on the point group. One of the
important previous results is that all symmetry-protected line nodes are
characterized by nontrivial topological numbers. Another intriguing discovery
is the gap structures depending on the angular momentum $j_z$ of normal Bloch
states on threefold and sixfold rotational-symmetric lines in the Brillouin
zone. Stimulated by these findings, we classify irreducible representations of
the Bogoliubov-de Gennes Hamiltonian at each $\boldsymbol{k}$ point on a
high-symmetry $n$-fold ($n = 2$, $3$, $4$, and $6$) axis for centrosymmetric
and paramagnetic superconductors, by using the combination of group theory and
$K$ theory. This leads to the classification of all crystal symmetry-protected
nodes (including $j_z$-dependent nodes) on the axis that crosses a normal-state
Fermi surface. As a result, it is shown that the classification by group theory
completely corresponds with the topological classification. Based on the
obtained results, we discuss superconducting gap structures in SrPtAs,
CeCoIn$_5$, UPt$_3$, and UCoGe.
