New supercharacter theory for Sylow subgroups in orthogonal and symplectic groups

Applying the embedding of $A_{n-1}$ in $B_n$, $C_n$ and $D_n$ we construct a new supercharacter theory for the Sylow subgroups in orthogonal and symplectic groups over a finite field. The constructed supercharacter appears to be a little bit more precise than the previously known one.