Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant theory and the W_{1+\infty} algebra with negative integral
  central charge   The vertex algebra W_{1+\infty,c} with central charge c may be defined as a
module over the universal central extension of the Lie algebra of differential
operators on the circle. For an integer n\geq 1, it was conjectured in the
physics literature that W_{1+\infty,-n} should have a minimal strong generating
set consisting of n^2+2n elements. Using a free field realization of
W_{1+\infty,-n} due to Kac-Radul, together with a deformed version of Weyl's
first and second fundamental theorems of invariant theory for the standard
representation of GL_n, we prove this conjecture. A consequence is that the
irreducible, highest-weight representations of W_{1+\infty,-n} are parametrized
by a closed subvariety of C^{n^2+2n}.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con