Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hitchin systems for invariant and anti-invariant vector bundles   Given a smooth projective complex curve $X$ with an involution $\sigma$, we
study the Hitchin systems for the locus of anti-invariant (resp. invariant)
stable vector bundles over $X$ under $\sigma$. Using these integrable systems
and the theory of the nilpotent cone, we study the irreducibility of these
loci. The anti-invariant locus can be thought of as a generalisation of Prym
varieties to higher rank.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex