Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multiplication of double cosets for $\GL(\infty)$ over a finite field   We consider a group $GL(\infty)$ and its parabolic subgroup $B$ corresponding
to partition $\infty=\infty+m+\infty$. Denote by $P$ the kernel of the natural
homomorphism $B\to GL(m)$. We show that the space of double cosets of
$GL(\infty)$ by $P$ admits a natural structure of a semigroup. In fact this
semigroup acts in subspaces of $P$-fixed vectors of some unitary
representations of $GL(\infty)$ over finite field.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci