Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum dimensions and irreducible modules of some diagonal coset vertex
  operator algebras   In this paper, under the assumption that the diagonal coset vertex operator
algebra $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak
g}(l,0))$ is rational and $C_2$-cofinite, the global dimension of
$C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(l,0))$ is
obtained, the quantum dimensions of multiplicity spaces viewed as
$C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak
g}(l,0))$-modules are also obtained. As an application, a method to classify
irreducible modules of $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes
L_{\mathfrak g}(l,0))$ is provided. As an example, we prove that the diagonal
coset vertex operator algebra $C(L_{E_8}(k+2,0),L_{E_8}(k,0)\otimes
L_{E_8}(2,0))$ is rational, $C_2$-cofinite, and classify irreducible modules of
$C(L_{E_8}(k+2,0),L_{E_8}(k,0)\otimes L_{E_8}(2,0))$.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
1
The categories of this paper are: cs