Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic connections on principal bundles over a Riemann surface   Let $E_G$ be a holomorphic principal $G$-bundle on a compact connected
Riemann surface $X$, where $G$ is a connected reductive complex affine
algebraic group. Fix a finite subset $D \subset X$, and for each $x\in D$ fix
$w_x \in \text{ad}(E_G)_x$. Let $T$ be a maximal torus in the group of all
holomorphic automorphisms of $E_G$. We give a necessary and sufficient
condition for the existence of a $T$-invariant logarithmic connection on $E_G$
singular over $D$ such that the residue over each $x \in D$ is $w_x$. We also
give a necessary and sufficient condition for the existence of a logarithmic
connection on $E_G$ singular over $D$ such that the residue over each $x \in D$
is $w_x$, under the assumption that each $w_x$ is $T$-rigid.

18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga