Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oppositeness in buildings and simple modules for finite groups of Lie
  type   In the building of a finite group of Lie type we consider the incidence
relations defined by oppositeness of flags. Such a relation gives rise to a
homomorphism of permutation modules (in the defining characteristic) whose
image is a simple module for the group. The $p$-rank of the incidence relation
is then the dimension of this simple module. We give some general reductions
towards the determination of the character of the simple module. Its highest
weight is identified and the problem is reduced to the case of a prime field.
The reduced problem can be approached through the representation theory of
algebraic groups and the methods are illustrated for some examples.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph