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Article overview
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On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a) | Frank Himstedt
; Tung Le
; Kay Magaard
; | Date: |
1 Aug 2015 | Abstract: | Let $UY_n(q)$ 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 $Irr(UY_n(q))$ of irreducible characters of $UY_n(q)$ 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 $UY_n(q)$ 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 $UY_n(q)$. 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 $Irr(UE_i(q))$, $6 le i le 8$ and
$Irr(UF_4(q))$. | Source: | arXiv, 1508.0050 | Services: | Forum | Review | PDF | Favorites |
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