Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Various generalizations and deformations of $PSL(2,\mathbb{R})$ surface
  group representations and their Higgs bundles   Recall that the group $PSL(2,\mathbb R)$ is isomorphic to $PSp(2,\mathbb R),\
SO_0(1,2)$ and $PU(1,1).$ The goal of this paper is to examine the various ways
in which Fuchsian representations of the fundamental group of a closed surface
of genus $g$ into $PSL(2,\mathbb R)$ and their associated Higgs bundles
generalize to the higher rank groups $PSL(n,\mathbb R),\ PSp(2n,\mathbb R),\
SO_0(2,n),\ SO_0(n,n+1)$ and $PU(n,n)$. For the $SO_0(n,n+1)$-character
variety, we parameterize $n(2g-2)$ new connected components as the total space
of vector bundles over appropriate symmetric powers of the surface and study
how these components deform in the $SO_0(n,n+2)$-character variety. This
generalizes results of Hitchin for $PSL(2,\mathbb R)$.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc