Characters of the Sylow p-Subgroups of the Chevalley Groups D₄(pⁿ)

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Let U(q) be a Sylow p-subgroup of the Chevalley groups D₄(q) where q is a power of a prime p. We describe a construction of all complex irreducible characters of U(q) and obtain a classification of these irreducible characters via the root subgroups which are contained in the center of these characters. Furthermore, we show that the multiplicities of the degrees of these irreducible characters are given by polynomials in q-1 with nonnegative coefficients.