Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic groups as difference Galois groups of linear differential
  equations   We study the inverse problem in the difference Galois theory of linear
differential equations over the difference-differential field $\mathbb{C}(x)$
with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main
result is that every linear algebraic group, considered as a difference
algebraic group, occurs as the difference Galois group of some linear
differential equation over $\mathbb{C}(x)$.

14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph