Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant and coinvariant spaces for the algebra of symmetric
  polynomials in non-commuting variables   We analyze the structure of the algebra N of symmetric polynomials in
non-commuting variables in so far as it relates to its commutative counterpart.
Using the "place-action" of the symmetric group, we are able to realize the
latter as the invariant polynomials inside the former. We discover a tensor
product decomposition of N analogous to the classical theorems of Chevalley,
Shephard-Todd on finite reflection groups.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs