Characters of the Sylow p-Subgroups of the Chevalley Groups D_4(p^n)

Details Characters of the Sylow p-Subgroups of the Chevalley Groups D_4(p^n) Characters of the Sylow p-Subgroups of the Chevalley Groups D_4(p^n)

2009-11-11

arxiv.org/abs/0911.2163v1

Mathematics

Representation Theory

Scientific paper

Let $U(q)$ be a Sylow $p$-subgroup of the Chevalley groups $D_4(q)$ 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.

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