Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On counting orbits in root systems   The computation of the characters of supercuspidal representations of a
p-adic group involves some 4th roots of unity whose values are defined in terms
of orbits of the Galois group of a p-field on a root system. The part of the
definition that is of interest in the verification of stability of character
sums involves just the parity of the number of Galois orbits. In this paper, we
re-cast the definition (nearly) in terms only of the abstract action of a pair
of automorphisms on a root system, and compute it by a series of reductions in
all cases.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics