Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Involutions of Iwahori-Hecke algebras and representations of fixed
  subalgebras
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas