Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Writing representations over minimal fields   The chief aim of this paper is to describe a procedure which, given a
$d$-dimensional absolutely irreducible matrix representation of a finite group
over a finite field $\mathbb{E}$, produces an equivalent representation such
that all matrix entries lie in a subfield $\mathbb{F}$ of $\mathbb{E}$ which is
as small as possible. The algorithm relies on a matrix version of Hilbert's
Theorem 90, and is probabilistic with expected running time ${\rm
O}(|\mathbb{E}:\mathbb{F}|d^3)$ when $|\mathbb{F}|$ is bounded. Using similar
methods we then describe an algorithm which takes as input a prime number and a
power-conjugate presentation for a finite soluble group, and as output produces
a full set of absolutely irreducible representations of the group over fields
whose characteristic is the specified prime, each representation being written
over its minimal field.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph