Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace functions and fusion rules of diagonal coset vertex operator
  algebras   In this paper, irreducible modules of the diagonal coset vertex operator
algebra $C(L_{\mathfrak{g}}(k+l,0),L_{\mathfrak{g}}(k,0)\otimes
L_{\mathfrak{g}}(l,0))$ are classified under the assumption that
$C(L_{\mathfrak{g}}(k+l,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(l,0))$
is rational, $C_2$-cofinite and certain additional assumption. An explicit
modular transformation formula of traces functions of
$C(L_{\mathfrak{g}}(k+l,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(l,0))$
is obtained. As an application, the fusion rules of $C(L_{E_8}(k+2,0),
L_{E_8}(k,0)\otimes L_{E_8}(2,0))$ are determined by using the Verlinde
formula.

32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom