Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining Aschbacher classes using characters   Let $\Delta\colon G \to \mathrm{GL}(n, K)$ be an absolutely irreducible
representation of an arbitrary group $G$ over an arbitrary field $K$; let
$\chi\colon G \to K\colon g \mapsto \mathrm{tr}(\Delta(g))$ be its character.
In this paper, we assume knowledge of $\chi$ only, and study which properties
of $\Delta$ can be inferred. We prove criteria to decide whether $\Delta$
preserves a form, is realizable over a subfield, or acts imprimitively on $K^{n
\times 1}$. If $K$ is finite, this allows us to decide whether the image of
$\Delta$ belongs to certain Aschbacher classes.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol