Polynomial properties of unipotent radicals of parabolic subgroups in classical groups

Abstract

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

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