Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A categorification of the boson-fermion correspondence via
  representation theory of $sl(\infty)   In recent years different aspects of categorification of the boson-fermion
correspondence have been studied. In this paper we propose a categorification
of the boson-fermion correspondence based on the category of tensor modules of
the Lie algebra $sl(\infty)$ of finitary infinite matrices. By $\mathbb T^+$ we
denote the category of "polynomial" tensor $sl(\infty)$-modules. There is a
natural "creation" functor $\mathcal T_N: \mathbb T^+\to \mathbb T^+$,
$M\mapsto N\otimes M,\quad M,N\in \mathbb T^+$. The key idea of the paper is to
employ the entire category $\mathbb T$ of tensor $sl(\infty)$-modules in order
to define the "annihilation" functor $\mathcal D_N: \mathbb T^+\to \mathbb T^+$
corresponding to $\mathcal T_N$. We show that the relations allowing to express
fermions via bosons arise from relations in the cohomology of complexes of
linear endofunctors on $\mathbb T^+$.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph