Polynomial properties of unipotent radicals of parabolic subgroups in classical groups

Let $R_u^{X,d}$ denote the unipotent radical of a (proper) maximal standard parabolic subgroup of the classical group ${\mathrm{S}\mathrm{p}}_{2n}(q)$, ${\mathrm{S}\mathrm{O}}_{2n}(q)$, or ${\mathrm{U}}_{2n}(q^2)$. This paper establishes explicit formulas for the number of irreducible characters of $R_u^{X,d}$ with degree $q^e$.