Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of the category O for W-algebras   W-algebra (of finite type) W is a certain associative algebra associated with
a semisimple Lie algebra, say g, and its nilpotent element, say e. The goal of
this paper is to study the category O for W introduced by Brundan, Goodwin and
Kleshchev. We establish an equivalence of this category with certain category
of g-modules. In the case when e is of principal Levi type (this is always so
when g is of type A) the category of g-modules in interest is the category of
generalized Whittaker modules introduced McDowel and studied by Milicic-Soergel
and Backelin.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ