Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relaxed highest-weight modules II: classifications for affine vertex
  algebras   This is the second of a series of articles devoted to the study of relaxed
highest-weight modules over affine vertex algebras and W-algebras. The first
studied the simple "rank-$1$" affine vertex superalgebras
$L_k(\mathfrak{sl}_2)$ and $L_k(\mathfrak{osp}(1\vert2))$, with the main
results including the first complete proofs of certain conjectured character
formulae (as well as some entirely new ones). Here, we turn to the question of
classifying relaxed highest-weight modules for simple affine vertex algebras of
arbitrary rank. The key point is that this can be reduced to the classification
of highest-weight modules by generalising Olivier Mathieu's theory of coherent
families. We formulate this algorithmically and illustrate its practical
implementation with several detailed examples. We also show how to use coherent
family technology to establish the non-semisimplicity of category $\mathscr{O}$
in one of these examples.

11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an