3,151 research outputs found
On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a)
Let be a Sylow p-subgroup of an untwisted Chevalley group
of rank n defined over where q is a power of a prime p. 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 1. 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
of . For 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 , and
On the characters of Sylow -subgroups of finite Chevalley groups for arbitrary primes
We develop in this work a method to parametrize the set of
irreducible characters of a Sylow -subgroup of a finite Chevalley group
which is valid for arbitrary primes , in particular when is a
very bad prime for . As an application, we parametrize
when .Comment: 22 page
The generic character table of a Sylow -subgroup of a finite Chevalley group of type
Let be a Sylow -subgroup of the finite Chevalley group of type
over the field of elements, where is a power of a prime . We
describe a construction of the generic character table of
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