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be a Sylow
-subgroup of an untwisted Chevalley group
is a power of a prime
. We partition the set
of irreducible characters of
into families indexed by antichains of positive roots of the root system of type
. We focus our attention on the families of characters of
which are indexed by antichains of length
. Then for each positive root
we establish a one-to-one correspondence between the minimal degree members of the family indexed by
and the linear characters of a certain subquotient
our single root character construction recovers, among other things, the elementary supercharacters of these groups. Most importantly, though, this paper lays the groundwork for our classification of the elements of
$6\leqslant i\leqslant 8$
For all prime powers
we restrict the unipotent characters of the special orthogonal groups
to a maximal parabolic subgroup. We determine all irreducible constituents of these restrictions for
and a large part of the irreducible constituents for
We compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of the simple Ree groups 2F4(q2). For one of the maximal parabolic subgroups, we find an irreducible character of the unipotent radical that does not extend to its inertia subgroup.
We compute the conjugacy classes and character table of a Borel subgroup of the Ree groups 2F4(22n+1) for all n ≥ 1 and prove that these Borel subgroups are M-groups. We determine the degrees of the irreducible characters of the Sylow-2-subgroups of 2F4(22n+1) and show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for 2F4(22n+1) in characteristic 2. For most of the calculations we use CHEVIE.
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