On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a)

Abstract

Let $U{Y}_n(q)$ be a Sylow p-subgroup of an untwisted Chevalley group $Y_n(q)$ of rank n defined over ${\mathbb{F}}_q$ where q is a power of a prime p. We partition the set $Irr(U{Y}_n(q))$ of irreducible characters of $U{Y}_n(q)$ into families indexed by antichains of positive roots of the root system of type $Y_n$. We focus our attention on the families of characters of $U{Y}_n(q)$ which are indexed by antichains of length 1. Then for each positive root $\alpha$ we establish a one to one correspondence between the minimal degree members of the family indexed by $\alpha$ and the linear characters of a certain subquotient ${\overline{T}}_{\alpha }$ of $U{Y}_n(q)$. For $Y_n=A_n$ our single root character construction recovers amongst other things the elementary supercharacters of these groups. Most importantly though this paper lays the groundwork for our classification of the elements of $Irr(U{E}_i(q))$, $6\le i\le 8$ and $Irr(U{F}_4(q))$.

References in corpus (1)

• The generic character table of a Sylow $p$-subgroup of a finite Chevalley group of type $D_4$

Cited by in corpus (1)

• Character tables of Sylow $p$-subgroups of the Steinberg triality groups ${}^3{D}_4(q^3)$