Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On paired root systems of Coxeter groups   This paper examines a systematic method to construct a pair of
(inter-related) root systems for arbitrary Coxeter groups from a class of
non-standard geometric representations. This method can be employed to
construct generalizations of root systems for a large family of groups
generated only by involutions. We then give a characterization of Coxeter
groups, among these groups, in terms of such paired root systems. Furthermore,
we use this method to construct and study the paired root systems for
reflection subgroups of Coxeter groups.

4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio