Rigid Surface Operators and Symbol Invariant of Partitions

The symbol is used to describe the Springer correspondence for the classical groups by Lusztig. We refine the explanation that the $S$ duality maps of the rigid surface operators are symbol preserving maps. We find that the maps $X_S$ and $Y_S$ are the same essentially. We clear up cause of the mismatch problem of the total number of the rigid surface operators between the $B_n$ and $C_n$ theories. We construct all the $B_n/C_n$ rigid surface operators which can not have a dual. A classification of the problematic surface operators is made.