Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Half the sum of positive roots, the Coxeter element, and a theorem of
  Kostant
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol